Logic doesn't always come into it - where's the logic in being anti-gay?
You said "If you're anti-gay, the logical position is to support transgenderism," now you are saying "logic doesn't always come into it."
Can you hear that flip-flopping sound? Flip, flop, flip, flop.
As for 'trans away the gay', here's an article from a few weeks ago about the Tavistock.
I don't have a Sunday Times subscription. The Spiked article says it's done to counteract homophobic bullying in some cases, but there's no evidence that this is common, there's no evidence that this is common among children from traditional conservative families, and there's no evidence that the majority of MRAs support children transitioning to counteract homophobic bullying. Certainly, if you do some digging around online (again, I won't link to MRA websites in case it breaches the rules), you will find plenty of MRAs who say some very hateful things about transgender people.
You should watch videos produced by MRAs and read their message boards; in order to oppose someone's position, understanding it first is absolutely essential. I read tons of stuff that I don't agree with.