I wonder if the very fact of shared trans identity is uncomfortable to them because it reminds them of something that, paradoxically, they talk about all the time while somehow wishing that it's not what they were.

This is so perceptive. Yeah, that's always the fly in the trans-ointment, isn't it? That the very identity which they demand respect for (or, more accurately, deference to), proclaim to have pride in, and generally WILL NOT STFU ABOUT... comes down to, "I cannot accept who I really am". Talk about cognitive dissonance! No wonder they're such a pissy, unpleasant bunch. They're perpetually trying to square the circle of living a lie AND making that a cause for celebration (somehow). Maybe that's why they're so toxic towards people like yourself: you remind them that they ARE living a lie... because you refuse to. And LGB people like you have worked hard, and taken a lot of risks, to openly be yourselves. Which makes their "I'm so PROUD of DENYING WHO I AM!1!" shtick look pretty pathetic... not to mention disgusting.