The arguments for: 1. "Homophobia" seems inaptly restricted to fearing gay persons, 2. "Gaycism" seems parallel to "racism."
Arguments against: 1. "-cism" is not a suffix. (Not that you can't have a new suffix. Just in the "-ism" family, there's "-aholism.") 2. "Gaycism" is too silly and the idea it's supposed to express is very serious. (People will wonder what's "gayce"? And the facile rhyming seems lightweight) 3. Why replace a word once you have a word? (The old word comes to mean what people use it to mean. It's pedantic to fret about the roots of a word once it's embedded.)
I say no. Disagree?
IN THE COMMENTS: Internet Ronin puts his finger on what was vaguely troubling me:
Transpose the "c" and "y" and it spells "Gacyism," as in John Wayne Gacy.