Good point.
When I first saw the argument, I thought their thought process was something like this:
"Militant homophobes often end up being homo, therefore militant transphobes often end up being trans."
But this argument has multiple flaws:
1. while there's enough gay homophobes to make it a funny ironic trend, it's not an actual rule – most homophobes aren't gay, duh
2. trans transphobes aren't a thing at all, at least to my knowledge
and with your argument, and therefore accounting for gender:
3. gay homophobes are usually males who are against other, gay males, but Rowling is female, and she mostly speaks about males, not females
So the "pooner Rowling" argument completely falls flat: unlike accusing random reverends of being gay, it has not even the slightest basis in reality.