To be pedantic, that's mixing latin (felis) with greek (philia). Not sure if there's a word already but you could do ailourophilia.
When I, too, learned this wasn't about cats I scrolled down to see what the proper term was. Thanks!
Or perhaps, depending on irony levels, three terms. One each in Greek and Latin which they use to describe themselves, and one in Greek and Latin others use to describe them.
How about "commixtiophobia". Commixtio = Latin for 'mixing', phobia = Greek for 'fear'