I'm going to jump in here. I won't speak for anybody else, as I'm not as extreme as some. Here is what I'm skeptical of:
That diagnoses of pre-pubescent or barely pubescent children, either by the DSM or GID, are accurate enough to warrant the administration of hormones to prevent (not merely delay) puberty as provided by, for example, the WPATH (Harry Benjamin) standards.
That's really it. There's a lot that I'm not skeptical about, including hormone treatments on adults (adults can legally consent), hormone treatments on infants born with ambiguous genitalia or the victim of circumcision accidents, and wearing different clothes with a different haircut, or the existence of the transgendered in general.
What I'd like to see evidence for is what I consider ridiculously extreme confidence in the accuracy of psychological diagnostic methods on children, to the extent that it is self-evident to many that the correct thing to do is give them hormones that will at least threaten and probably destroy their ability ever to have children for the rest of their lives. Not only that, but self-evident to the point that it is perverse and an indication of bigotry to withhold automatic assent.