At the outset, I want to make clear that I did not find an answer to the question "Why did 'denigrate' greatly increase in usage during the mid-20th century?"
Instead, my answer attempts to address a couple of secondary questions that the OP raises: (1) does denigrate have racist (or racially tinged) origins? and (2) did the rise in frequency of written occurrences of denigrate starting in the 1950s have a racial component?
Discussions of 'denigrate' in etymological dictionaries
Ernest Weekley, An Etymological Dictionary of Modern English (1921) has this brief entry for denigrate:
denigrate. From L[atin] denigrare, to defame, lit[erlly] to blacken. Obs[olete] in 18[th] cent[ury] and now revived in imit[ation] of F[rench] dénigrer.
Harrap's New Collegiate French and English Dictionary (1967) reports that dénigrer means "To disparage; to run down"—which suggests that the nineteenth- and early twentieth-century revival of denigrate was from the outset an allusion to metaphorical, not literal, blackening.
William Morris & Mary Morris, Morris Dictionary of Word and Phrase Origins (1977) has this:
denigrate most commonly means "to defame," but its basic meaning is "to blacken," either literally or figuratively. Denigration may be of one's character or of one's flesh, as a bruise darkens after physical injury. It comes from the Latin denigare, meaning "to blacken."
John Ayto, Dictionary of Word Origins (1990) has a somewhat more detailed entry for the word:
denigrate {16[th century]} To denigrate people is literally to "blacken" them. The word comes from the Latin dēnigrāre 'blacken,' a compound verb formed from the intensive prefix dē- and niger 'black.' This adjective, which is of unknown origin, also produced French noir 'black' and Italian nero 'black,' and is the source (via Spanish negro) of English negro {16[th century]} and the now taboo nigger {18[th century]}. Denigrate originally meant 'physically turn something black' as well as the metaphorical 'defame, belittle': 'This lotion will denigrate the hairs of hoary heads,' Richard Tomlinson, Renodaeus' Medicinal dispensatory 1657.
And finally, Glynnis Chantrell, The Oxford Dictionary of Word Histories (2002) offers this short entry:
denigrate {late middle English} Early use was recorded as 'blacken, make dark'. Latin denigrare 'to blacken' is the source, from de- 'away, completely' and nigrare (from niger 'black'). The sense has developed into the figurative 'disparage'.
Two early instances of 'denigrate' in U.S. newspapers
A search for denigrate in the Elephind newspaper database roughly 1,750 matches from the United States and Australia over the period 1850–2019. The earliest of these appears in Tim Basswood, "Oh That Mine Enemy Would Write a Book," in the Rutland [Vermont] Herald (April 18, 1850):
Spiteful attempts to denigrate character by innuendo or accusation, unsupported by any proofs, are unworthy of any notice, and perhaps should be permitted to rest in that obscurity into which they invariably fall. But our volunteer [writer of an earlier item in the Rutland Herald] must not escape on so easy terms, especially since he so uncerimoniously plunged into the same slough, out of which he so valiantly volunteered to extricate his unknown compeer.
And the next-earliest is from "The Argentine Republic," in the New York Herald (April 3, 1851), reprinted from the Buenos Ayres Packet (January 11, 1851):
In the Commercio del Plata of Montevideo, we have latterly observed a captious and unfounded theory on this point; showing an absolute ignorance, or, what would be worse, a gross and willful perversion of the elementary principles of economical science. In a series of articles on the Paper Money of Buenos Ayres, intended merely to denigrate the administration of General Rosas, the editor attempted to show the practicability, and consequent obligation, of remedying or alleviating the late crisis, by a system of loans to individuals from the Public Treasure.
Both of these instances use denigrate in a metaphorical sense, as one would expect from Weekley's account of its reemergence in the nineteenth century in imitation of dénigrer.
Instances of 'denigrate' from newspapers in the 1950s
To see whether a more literal—or racially tinged sense of the word may have contributed to its rise in frequency of use (according to Google Ngrams) during the period 1950–1970, I checked the context in which it appeared in each of the 26 unique instances of denigrate that an Elephind search identifies from the period 1950–1959. Here they are, in chronological order.
From "East-West Tug in Indo-China," in the [Melbourne, Victoria] Argus (February 1, 1950):
Russia's recognition of Ho Chih-minh is a swift move to denigrate France's ratification of an agreement that the States of Viet Nam, Laos, and Cambodia should have self-government within the French Union.
From "All We Need Is the Will," in the [Melbourne, Victoria] Argus (September 18, 1951):
Is there any reason, then, apart from habit, why we should continue to denigrate our own industrial achievements before those of other lands?
From A.J. Cummings, "Monty Seen as Man for the Job in Malaya" in the [Adelaide, South Australia] News (December 21, 1951):
Almost as soon as the war was over they began to write books and essays in which they sought to denigrate Montgomery's generalship in the field.
From "Column 8," in the Sydney [New South Wales] Morning Herald (December 31, 1951):
As a rule I don't denigrate women drivers, who seem to me to be as competent as men drivers and much more polite.
From "Tax Committee Is a Facade for Treasurer," in the Sydney [New South Wales] Morning Herald (October 13, 1952):
This is not to denigrate the committee. So far it has carried out its instructions with the application and skill to be expected from its distinguished personnel.
From "St. Alban's Notes," in the Muswellbrook [New South Wales] Chronicle (November 14, 1952):
The Archbishop of Canterbury recently said he had no time for those who went about denigrating their church. To denigrate is to blacken. Unfortunately, there are in every institution those who choose rather to denounce and criticise than assist.
From "Russia's Poison Campaign," in the [Adelaide, South Australia] Advertiser (December 23, 1952):
At the current meetings of UN, "those countries," as Sir Percy Spender phrases it, "which for various reasons have some responsibility for non-self-governing territories," have been, and are being, subjected to an outrageous series of attacks; and an international "security" organisation, sustained, as to 70 per cent of its cost, by themselves, is thus being used by their enemies to denigrate them, to brand them as "oppressors" and "exploiters" of defenceless savages, and, in general, to undermine them along what may be called the whole "moral front."
From A.J. Siggins, "Along the Colonial Front," in the Indianapolis [Indiana] Recorder (February 7, 1953):
Our missionaries have told Africans that their church is the only true one and the other missionaries are liars. I have heard missionaries saying these things. I have known many Africans who have been contemptuous of the attempts of Christian missionaries to denigrate their fellows.
From "Correspondence," in the [Rockhampton, Queensland] Morning Bulletin (April 22, 1953):
Far be it from me to seek to denigrate or even depreciate a singer from whose vocal efforts I derived enjoyment. Give credit to whom credit is due by all means.
From "Peace and War," in the [Adelaide, South Australia ] Advertiser (July 8, 1953):
This is the era of the so-called "peace offensive," a campaign conducted by means of lying propaganda by a State that desires either to conceal its own warlike intentions, or to denigrate and infuriate its neighbors.
From Jon Cleary, "The Climate of Courage," in the Sydney [New South Wales] Morning Herald (November 24, 1953):
The men were singing the Army version of "The Old Grey Mare," and it was possible to denigrate the company commander without lowering the troops' morale.
From William Morris, "Words, Wit & Wisdom," in the San Bernardino [California] Sun (March 18, 1954):
Today, though, when one castigates a rival, he merely criticizes him verbally. When you denigrate (pronounced DEN-ih-grayt) a person, though, you are doing him much more costly damage than mere criticism could effect, because denigration, from the Latin DENIGRO, to blacken, means to defame an opponent by blackening his character. Thus a historian might write: "In the sordid campaign of 1888, denigration of candidate's by their political fores became the order of the day."
From "Book Reviews," in the [Fort Hood, Texas] Armored Sentinel (August 12, 1954):
The British commanders were constantly under pressure to combat "the Rommel legend" and it is to their credit that they did nothing to denigrate his character but only to dispel the belief he was unbeatable.
From "The V.R.C. Versus Fitzgerald" in the [Melbourne, Victoria] Argus (November 4, 1955):
What must have happened, I think, is that your writer spent the day between the members' enclosure and the paddock, and has seized on certain unavoidable happenings there to denigrate the whole racecourse.
From a review of What Manner of Man Was Moses? in the [Indianapolis, Indiana] Jewish Post (December 30, 1955):
It is always pleasing to peruse a book about Moses which does not denigrate his work and character.
From Harold Milks, "Krushchev in New Attack on the West" in the Santa Cruz [California] Sentinel (November 19, 1956):
Of Egypt [Khrushchev said]: "The Western powers are trying to denigrate Nasser . . . The situation Is serious and we are realists. The fire must be put out. 1 think the British and French will be wise enough to withdraw their forces and then Egypt will emerge stronger than ever."
From "Eisendrath Says POST for Wholesale Migration," in the [Indianapolis, Indiana] Jewish Post (April 26, 1957):
However, to be perfectly certain that this will not be the case, I should like to reply to what I regard as your distressing column under the "Editor’s Chair*" on Friday, March 1, 1957, in which you denigrate the future of the American Jewish community and pull out all the stops for wholesale emigration to Israel on the part of American Jews by quoting, at some length, from one whose zeal for Zion can in no wise be challenged.
From a review of The Sabbath Book in the [Indianapolis, Indiana] Jewish Post (May 31, 1957):
There is no effort to denigrate the Jewish Sabbath law, as is often the manner of the Jewish "liberal," hence the traditionally minded, too, will find joy and comfort in its perusal.
From "LeBrun Discusses Current Paintings," in the [Poughkeepsie, New York] Vassar Miscellany News (December 10, 1958):
LeBrun's belief in the "world of images" and the universal truths to be found therein prompt him to criticize and denigrate the action painters and the abstract-expressionists.
From "Lessons in English" in the Madera [California] Tribune (March 19, 1959):
Today's word: DENIGRATE; to biacken: hence, to sully; to defame. (Accent first syllable). "Every leader has certain ones among his followers who attempt to denigrate him."
From Donald McDonald, "Intellectuals, Iowa, Women," in the Pittsburgh [Pennsylvania] Catholic (May 21, 1959):
Well, the anti-intellectual tide seems to have spent itself. At least in the last few years, voluntarism, demagoguery and emotionalism have quieted considerably. It is no longer quite so fashionable to denigrate the human mind[.]
From Don Foskett, "Happy Would Have Given the Folks a Show," in the [Hartford, Connecticut, Catholic Transcript (July 23, 1959):
His intent may not have been to denigrate Landis as much as it was to glorify Chandler, but the effect was to give the impression that the judge wasn't very bright about a number of things.
From "Science Cannot Change Right and Wrong," in the [Hartford, Connecticut, Catholic Transcript (October 8, 1959):
"To slight the returning patient, to denigrate him, to render him unwelcome," warns Dr. Braceland, "is to cause him to regress and even to prefer the hospital to the community which rejects him."
From William Ready, "Authors Readable and Benign," in the [San Francisco, California] Monitor (November 13, 1959):
So scornful and contemptuous was he [Hilaire Belloc] of many whom he both opposed and defended that those in power in the literary field have conspired to keen silent about him or to denigrate him. Upon his death the obituaries often were spiteful.
From Sidney Morgenbesser, "Man, the State, and a Theory of War" in the [New York City] Columbia [University] Daily Spectator (November 20, 1959):
To cast doubt upon the utility of the quest for a general theory of war is neither to denigrate the role of theory in social science nor to embrace the position that laws and theories play no role in historical explanation.
From "A Close Look at POAU," in the [Hartford, Connecticut] Catholic Transcript (December 17, 1959):
It is hardly conceivable that at this late date one needs to explain that the initials POAU refer to an organization which calls itself Protestants and Other Americans United for Separation of Church and State. No more can it be required to tell reasonable and critical people that the group is rabidly anti-Catholic, and, on the record, has no aim hut to denigrate the Catholic Church and relegate Catholic Americans to the rank of second-class citizens.
Some thoughts on the sample instances
One interesting aspect of these results is that ten of the first eleven instances (from 1950 through 1953) are from Australian newspapers, and fourteen of the last fifteen instances (from 1954 through 1959) are from U.S. newspapers. I don't have a ready explanation for this split. On the one hand, it is quite striking; but on the other, it may be that the source materials that Elephind uses in its searches are heavily skewed toward Australian newspapers the early 1950s and toward U.S. newspapers in the later 1950s. In any case the sample size is extremely small, and it would be unwise to draw any large conclusions from its contents.
A second noteworthy feature of the results is that there are very few instances in this sample where denigrate appears in the context of race. Two of the instances, in fact, are simply discussions of what the word means. Of the other twenty-four, the objects of denigration include French ratification of a colonial treaty, Australian industrial achievements, General Montgomery's generalship, women drivers, a local treasury committee, the Church of England, colonial powers, missionaries (by fellow missionaries), a singer, neighboring countries, a military commander, General Rommel's character, a racetrack, Moses, President Nasser of Egypt, the American Jewish community's future, Jewish Sabbath law, action painters and abstract expressionists, the human mind, a former commissioner of major league baseball, a patient from a mental hospital, Hilaire Belloc, the role of theory in social science, and the Catholic Church.
These results are not what you'd expect to encounter during a critical period in a word's popularization if that word were being used in an implicitly race-conscious way. Again, the sample size is tiny—but even so, I don't see even a hint of racial signaling in any of the individual instances here.
Conclusions
During its earlier period of use in English (prior to becoming obsolete in the eighteenth century), denigrate sometimes conveyed the meaning of physical (or visual) blackening, as John Ayto illustrates in his example from 1657. The dictionaries I consulted, however, do not suggest that this sense of physical blackening was centrally—or even peripherally—associated with racial skin tone.
Ernest Weekley, writing in 1921—decades after the word's reappearance in English, but well before the period 1950–1970 when its frequency of occurrence in published works began to rise sharply, according to Google Ngram—asserts that denigrate made its comeback as a term with a strictly figurative sense of blackening, not a literal one. He further argues that English speakers who revived it in the 1800s did so in imitation of the French verb dénigrer, whose meaning in French may have become wholly figurative by that time.
If Weekley's position is correct, we should expect to see figurative (not literal) uses of denigrate in early instances of the revived term, and we should expect not to see strong evidence of a racial component in subsequent usage of the term—unless users at some point after 1921 altered the sense of the term to move it in a racial direction.
The results of my extremely small-scale research into usage of denigrate in the early 1850s and in the 1950s are consistent with Weekley's analysis. Obviously, however, they are too small to offer anything more than anecdotal evidence of how some English speakers in the 1850s or in the 1950s understood the word and its overtones.