No. 'Homosexualism' is a proper word.
'Homosexualist' is listed by Wiktionary as an alternative to the term 'homosexual', referencing the Oxford English Dictionary, and giving usage examples as early as '49... albeit that the term smells a bit arcane. It's use is legitimate in any case, as an 'ist' is generally a practitioner of an 'ism'... True enough that 'ist' is used as a bolt-on component even where the word proper does not exist, conveying the thought of a single practitioner of a thing.
And it is in popular use, as can be seen by plugging the word into a search engine. No doubt it's popular use predates FR.
Both are words, both are found in abundance upon the web.
caver's comment holds no merit, even if withholding it's vituperation.
Thanks for the info, roamer.
My sense is that “homosexualism” now substitutes as a synonyn for “gay agenda.” Homosexualism, as with communism, is advocacy of a particular philosphy.