I don’t think you’re talking about fear, you’re talking about hatred. The word you want would be transmisia, not transphobia. And even that is problematic because “trans” is an amputation of either transsexual or transvestite, two very different groups of people, the latter of whom don’t in my opinion deserve a lot of bending over backward.
You and everyone discussing this issue should drop the silly neologisms and all the cis- stuff and just say “prejudice against transsexuals.”
I’m not sure that whatever Rowling did is worth a lot of heat and light. Her children’s books were a long time ago now and she’s receding in the rear view mirror.
I’d worry more about choosing your battles a little more wisely. The Pronoun Police are irritating and detract from actual, you know, prejudice.