If it's a specific art piece whose content he doesn't want to produce but he's willing to otherwise serve the customer, I'm fine with that.
That's not what's going on with this baker.
https://en.oxforddictionaries.com/definition/homophobia
homophobia
Dislike of or prejudice against homosexual people.
I'll also note that the above falls neatly withing "aversion to something", which was part of your cited definition, but you skipped that bit apparently.
If you're going to complain that other people don't know what words mean, make real sure you're in the right, bucko.