When did "call out" become so widely used as in:
To combat authoritarianism, to call out lies, to struggle honorably and fiercely in the name of American ideals
(from the New Yorker)
Although 'to call out' in the sense of 'to challenge, confront' has been in use since at least the late 1600s, early uses are limited to uses with the added sense of 'to challenge to a fight', and especially to a duel. Thus, early uses refer in the main to physical combat, rather than verbal. I will assume for purposes of restricting the scope of the answer that the question is about the later and contemporary uses with this more restricted sense:
to call out
b. orig. and chiefly U.S. To expose or identify (a person) as acting in a dishonest or otherwise unacceptable manner; to challenge or confront. ....
["call, v.". OED Online. September 2016. Oxford University Press. http://www.oed.com/view/Entry/26411?rskey=kq8Wyb&result=1&isAdvanced=true (accessed November 17, 2016).]
Attestations from 1981 to 2013 are shown for 'to call out' sense 4b.
Note that the OED muddies the otherwise limpid lexical waters by tacking a cross-reference onto definition 4b (of 'to call out'): "Cf. to call on —— 5 at Phrasal verbs 2."
to call on ——
5. trans. orig. and chiefly N. Amer. To challenge or confront (a person) over his or her dishonesty or unacceptable behaviour. ....
Attestations from 1944 to 2006 are shown for 'to call on' sense 5.
Furthering my goal of limiting complexity in the answer, which could easily become unwieldy, I will ignore the interconnections of these senses of 'to call out' and 'to call on' and focus only on documented recent upticks in the use of 'to call out' sense 4b.
The question asks "when" 'to call out', in the sense exampled, became "so widely used", thus assuming that it has become more widely used.
Evidence in the NOW Corpus (News on the Web) from 2010 to 2016 for the phrase "call * out" suggests the assumption in the question is correct, although the increased frequency is not overwhelming, and the evidence is not as clearcut as could be hoped.
Setting aside for the moment the question of how clearcut the evidence is, that is, how many of the tokens charted are uses of 'to call out' in sense 4b, the usage peaks seem to calibrate to contentious US primaries and elections. For example, a peak of 0.66 per million occurs in the first half of 2012, the run-up to a contentious US presidential election; another, lesser peak of 0.56 builds into the last half of 2014, the run-up and aftermath of bitter mid-term elections; another peak of 0.68 builds into the last half of 2015 (off-year elections); yet another peak has built through the first half and approximately 4.5 months of data for the last half of 2016.
That peaks and troughs of usage appear to correlate with US election cycles, however, says nothing about cause-and-effect. Any number of other apparent correlations, including correlations having nothing whatsoever to do with US election cycles, might be superimposed on the data.
What is telling, in terms of the question at hand, is the overall increase in frequency of use of 'to call out'. Aside from the outliers of 0.59 in the last half of 2011, 0.66 in the first half of 2012, and 0.58 in the last half of 2012, frequency per million words of corpus data has not risen above 0.56 — until a sustained frequency over 0.62 began with 0.68 in the last half of 2015 and is on track to continue through at least 2016.
When 'to call out' became more widely used might, on the basis of the raw NOW Corpus data as presented and analyzed so far, be said to have been the last half of 2015. It remains to be seen, however, what percentage of the uses charted are uses in sense 4b.
First, note the pattern of uses for various replacements of the "*", as charted above. I've checked the phrases I consider likely to often although not invariably be uses in sense 4b:
Without belaboring the point, a rapid scan of the context of the checked phrases in 2016 establishes that the predominant usage is in sense 4b. Here are the most recent 25 uses in the corpus:
As a check for bias, varying the parameters of the corpus search produces similar, if not more striking results. For example, a search for "call out" (without an inserted replacement term), returns this chart:
The context of uses for 'to call out' without a replacement token, however, shows the simple phrase "call out" is not predominantly used in sense 4b. Only five of the most recent twenty-five instances were clearly uses with the 'to challenge or confront' sense.