As a trans* person, trans* doll characters offend me. The issue of gender is not your plaything. Stop treating it like a trend/fetish.
This is probably going to go into some potentially un-PC territory, and I’m sorry in advance. I’ll try to tread lightly.
I’m not trans*, but my brother is, and I’ve got one character who presents as trans*, but who hasn’t been shelled into a doll yet. Boss is complicated and presents and identifies publicly according to outdated terminology and isn’t in a time/place to reconsider those things, and isn’t the type of character who adjusts his behavior unless it suits him above anyone else’s comfort level. (For reference, I mostly use ‘him’ pronouns-wise with him, even though he predominantly presents as female, because where he is in-story, it’s more advantageous for other people to parse him as male/dominant/in power, and the English language is tricky, and he hasn’t figured out or acknowledged neutral pronouns yet. Boss is strange and potentially offensive, so I usually play him in closed circles.)
I don’t think trans* characters are inherently offensive, but I do think they’re tricky to pull off in the doll world—I rarely see people whose characters don’t pass, or whose narratives involve struggling with surgical/hormonal transition; the dolls I’ve seen are mostly pre-op, pre-hormones, and are in the “my body and my identity don’t align, and it gives me angst, but I haven’t taken steps to do anything to rectify it” stage. I’ve never encountered someone whose doll had a trans* narrative, but was post-op and passing, or post-op and not passing. They’re alway pre-op. (…And always MtF, if I find them at all.)
With dolls you functionally have three choices; buy your doll’s birth-sex-assigned-body, buy your doll’s post-op body, or mod one or the other to represent the middle ground. You can dress your doll however you’d like, regardless of the body you buy it, and most people won’t have a clue unless it becomes a plot point or you bring it up in discussion. People constantly get dolls’ genders wrong at a glance, because unless your doll’s got genitalia showing, the odds of guessing based on sculpt/faceup/wig/clothes aren’t actually that great.
That said, though, it’s really easy for people to misrepresent groups they don’t have extensive personal experience with—the issue of gender is a big minefield; there are a lot of people who will insist that their experience is the only valid one, and that any other interpretation is “wrong”, and that makes writing non-binary characters really complex and difficult. Where Boss doesn’t offend my brother (no doubt in part because he’s helped me tweak and develop him over the years), I know other people who absolutely would find him offensive, because he (as a character) isn’t always a “positive” representation, and he certainly isn’t progressively-minded. (My primary defense for this is that he was born in the 60s or 70s and is kind of a shithead to begin with.)
tl;dr OP, I’m sorry you’re offended—gender is a complicated, messy subject, just like sexuality or religion can be—but I disagree that people exploring those concepts is offensive by default. :<