I concur with Edwin Ashworth's observation/conclusion that prioritize and prioritise are in common use today, far afield from government work. The following Ngram chart tracks the rise of prioritize (blue line) and prioritise (red line) over the period 1950–2007:

A Google Books search of either spelling yields numerous matches for the word, in content that targets audiences ranging from business to government to academic to self-help.
Easily the earliest match for prioritize in the Elephind newspaper database comes from William Morris, "Words, Wit & Wisdom" in the San Bernardino [California] Sun (November 9, 1954)—a column dedicated to government "officialese" and neologisms. Here is the relevant paragraph:
Another tendency noted among government workers on both sides of the Atlantic is the trend toward making verbs of nouns and adjectives by adding "-ize." "Finalize" and "concretize" are two such barbarisms which made their first appearance in the shop-talk of the advertising business shortly after the last war. Now they seem—according to this column's Washington operative, Jack E. Grant—to be firmly embedded in the speech of government workers, along with "civilianize" (replace military personnel with civilians) and "prioritize" (give preferential rating to).
If this news piece is correct, prioritize originated as advertising jargon, at some point between 1945 and 1954, and migrated from there into bureaucratic language. William Morris was a co-author, with Mary Marris, of Dictionary of Word and Phrase Origins (1962), but that book does not include an entry for prioritize.
Morris treats prioritize and civilianize as equally outlandish recent coinages, suggesting that he expected both words to be unfamiliar to the vast majority of his readers. Somewhat surprisingly, Merriam-Webster's Eleventh Collegiate Dictionary (2003) lists the date of first known occurrence of prioritize as 1964:
prioritize vt (1964) to list or rate (as projects or goals) in order of priority.
A usage note under the same dictionary's entry for the suffix -ize merits quotation in full:
usage The suffix -ize has been productive in English since the time of Thomas Nashe (1567–1601), who claimed credit for introducing it into English to remedy the surplus of monosyllabic words. Almost any noun or adjective can be made into a verb by adding -ize {hospitalize} {familiarize}; many technical terms are coined this way {oxidize} as well as verbs of ethnic derivation {Americanize} and verbs derived from proper names {bowdlerize} {mesmerize}. Nashe noted in 1591 that that his -ize coinages were being criticized, and to this day new words ending in -ize {finalize} {prioritize} are sure to draw critical fire.
The real mystery, I suppose, is why English speakers haven't adopted nasheize as a verb meaning "to transform a noun or adjective (especially a monosyllabic one) into a verb, by adding -ize to it."
As a final note I should point out that the Google Books match supposedly from 1950—Warren's Weed on the New York Law of Real Property, Volume 5—which the original poster of this question cited as a confirmed early occurrence of the term—is misdated, as can be seen by reading the paragraph preceding the one that appears in the posted question:
Law 1985, ch. 38 § 12, effective April 16, 1984, also amended Environmental Conservation Law § 27-1305(4) by adding two new subparagraphs, (e) and (f), as follows:
e. The department shall, in consultation with the department of health, evaluate existing site evaluation systems and shall develop a system to select and prioritize sites for remedial action. Such system shall incorporate environmental, natural resource and public health concerns.
The quoted language from subparagraph (e) thus appears to have been formulated not long—and certainly not decades—before April 1984.