Being transexual has nothing to do with her character, AND THAT's what i dont like.
I would argue that that's EXACTLY how it should be - being trans is just one small aspect of who she (and other transgendered people) is as a person. If you don't like the rest of who she is, so be it, but that's pretty much a separate issue.
I agree for the most part the only part I find weird is how she outright outs herself. Like it felt inorganic, like it was just an initial statement "Hey kids look we have diversity!" without doing anything with that diversity. It'd be like if instead of Tai talking about girlfriends and hooking up with girls in an organic sense she'd be like "Yeah I like girls" but then never date girls, express interest in girls. Like I felt like a more organic way of showing Clare was trans without making it about trans-issues could've been done like offhand comments about transition or side conversations.
Maybe it's just me, but I've never had a one-size-fits-all outing experience. When people have come out to me in one way or another, I don't think there's a little manual somewhere that they consulted first. Never having been on their side of the situation, I can only guess/empathize that it probably involved a bit of mental calculus as to how "safe" it'd be to come out to me, how I might react, what I might or might not tell other people, and a whole host of other stuff that I'm probably totally missing because, again, that's not my lived experience.
With that being said, for me (again, speaking from my own limited experience), something about Claire's coming out to Marten rang true to me. It wasn't played for shock value, or as an exploitative plot hook. To me, it read as someone deciding she trusted someone else enough to come out to him, and maybe fumbling with it a bit because hey, it's awkward sometimes, and you also never know how the other person's going to take it.
The point is, people come to that point in a way that feels right to them (or at least as close to right as they can get, depending on circumstances). The timing, the words, and all the rest aren't always what they'd planned or what you'd expect -- sometimes blunt, sometimes very circumspect; sometimes eloquent, others halting -- but that's just how life is sometimes. It's not always going to be in a way that fits some grand narrative arc or some dramatic reveal; life ain't always like the movies. Similarly, sometimes our fiction ends up being as untidy as life itself.
Hope this gets my point across, even if it's not as well put as I'd like.