No, they need to ban it because deep down they are afraid they are trans and if they can somehow ban it then they can keep pushing those feelings down and ignore it.
They literally did lose the war on gay acceptance. It became politically infeasible for conservatives to run on anti-gay platforms. That's the entire reason they switched all of their efforts towards trans people.
Now, do they plan to come after gay people once they've annihilated trans people? Absolutely. There is no chance they have forgotten about them as their ideology does not allow minorities to exist as equals and they are 100% using trans people as their foot in the door to eventually come after everyone else.
I read your comment as they want to hook up with trans people and I was adding that some (most?) are trans themselves and repressing it. I think it's probably important to recognize both of those potential aspects of where trans hate can come from.