Besides all the excellent points that you make, the knee-jerk response that a strongly homophobic person must be secretly gay often distracts from the real issues involved.
I write about LGBTQ issues all the time, often focusing on injustice. So I get comments every day about the subject, and every day a large percentage of them are assertions that somebody perpetuating injustice just has to be a closet case.
I might have spent three or four days looking into a matter and coming up with a pretty detailed analysis of what's going on. And it all gets reduced in public commentary too, "check the guy's browser history" or "you can bet your ass somebody's going to find that guy in a motel room one day with a crack pipe and a rent boy."
Persecution of LGBTQ people is not driven primarily by secretly gay people. It's driven by people who believe certain things and act on those beliefs.
We do ourselves harm by not acknowledging that and working from that knowledge.