Marten and Vicky thought nothing of disclosing the trans* status of her friends to Faye in a jokey, cavalier way. Why would he hesitate to do the same vis a vis Claire (in a situation that involved him much more directly and presently) unless he had substantially rethought his position?
Because discussing people who are already out (in this case the drag queens from Marten's past), is different from someone who is obviously telling you a very close kept secret (in this case Claire). It's the abstract issue of saying "a lot of the girls I thought I was hanging out with were actually my mom's drag queen friends" and "hey, did you know that Claire, the specific individual person is trans?" They are not equivalent things in the realm of information given. Marten didn't name any of those men specifically, he just commented that a lot of them happened to be men. And the fact that he was sort of weird about that, doesn't mean he was anti-trans, or unsympathetic to trans issues. It just means that he was awkward trying to flirt with someone who he thought might be female, because he is apparently attracted to women, and then finding out they were actually men in disguise. Being uncomfortable about that surprise revelation is totally different from being anti-trans.
And since you have previously cited that strip where Dora jokingly suggests she's actually a guy, just to mess with Marten's head, you could easily say that she's just as anti-trans as you think Marten used to be. Her statement implies (in theory at least, I'm playing devil's advocate here), that there is something wrong with that revelation, and she knows it, otherwise she wouldn't have used it as a way to try and get a dig into Marten. Jokingly or not. Also, when she beat Faye over the head for potentially "scaring Marten over to the gay side", implying there is something wrong with that. Those statements were made for comedic value, and don't necessarily suggest that someone is anti-anything.
If I was dating a woman, and had already been in an intimate relationship with her, and she came out and said "Oh yeah, by the way, I was born a guy but I had surgery/treatments to swap genders" It would shatter my mind too. And guess what, I'm totally fine with transgender people. It would be a shock that would have to be dealt with. The sudden revelation about something that was kept from you, possibly feeling betrayed that they didn't tell you before anything got far in the relationship, how that impacts who you are and who you see yourself as. To say that it would fuck with your head, as Marten said, is a perfectly natural response, to the scenario that Dora presented. It doesn't mean that he has any issues with trans people. Besides, I'm pretty sure that Tai doesn't know that Claire is trans anyway, so I don't see how hanging out with her would make Marten be more Pro-trans than before. If you are implying it's because of her lesbian nature, well he grew up around gay people all the time, and hung out with them. So I would say it's still not because of Tai, and still say it's because Marten is actually just a good guy, who isn't the kind of guy who would "out" anyone about anything they confessed to him in a trusting way. It doesn't have anything to do with being around anyone, it's just how he is.
Marten was made aware of Claire's nature as a trans when they were still just friends, and so the development of his feelings for her from the start, were coming from a place of understanding about who she is. Which (I think), is why he isn't worried about it. It was a soap opera-esque drama bomb, laid in his lap mid relationship (cue dramatic organ music, and fade to commercial), it was simply stating a fact up front. He accepted it like he does everything else about his friends, with an open mind, and no judgement. The attraction came after because of that honesty, not because he works with a free-spirited lesbian.