If he isn't put off by their trans status, then I wouldn't necessarily say he's bisexual, I'd say he's open minded and willing to experiment with and test his sexuality and boundaries perhaps. I think active attraction is important in defining someone's sexuality, not simply the lack of revulsion.

Eh I disagree. He's still engaging with a man and no amount of makeup, long hair, perfume, and provocative clothing or even having your penis shoved inside out is gonna change that. There is a word though and that is Gynephelia. Gynephelia is the attraction to femininity regardless of sex (And the opposite of this is Androphilia which is the attraction to Masculinity regardless of sex). These two specifics are definite things in a lot of bisexual people. for example a bisexual guy who is attracted to feminine women and feminine men ("Transwoman" included) but is not attracted to masculine men or masculine woman, that would be a case of Gynephelia at play here. Or take a Bisexual woman who is attracted to masculine men and masculine women ("Butches", "Studs", etc.) but has no interest in feminine women or feminine men, that would be a case of Androphilic bisexuality.

If a man believes a transwoman is a biological woman, he's thinking of a biological woman when he sleeps with her.

Yeah no. Again I've seen what these kinds of dudes say and they are the ones who equate femininity to define women and that is not what being a woman is. Femininity does not define woman and what you're seeing is self-internalized homophobia at work there. He's trying to justify sexing/dating a hyper feminine man but doesn't want to acknowledge it for a variety of reasons that have to do with self-internalized homophobia. Now agian, this isn't saying that the guy is gay but self-internalized homophobia is a big thing among bisexual men because they can go all their formulate years thinking they can't be attracted to other men because they're only attracted to women and haven't seen a man (feminine and I don't just mean by mannerisms, I'm talking full on feminine presenting men in addition and think about it, how many super feminine presenting boys did you see when you were in school? Most likely not all that many to even none at all. At least not as much compared to say a tomboy) until they get older and come across these kinds of men and thus they experience their what I call, "Bi Awakening". The man can "believe" all he wants that the "transwoman" he's seeing is still a woman but it doesn't change biological reality that he's with another dude.

A transman can look as manly as possible, but knowing there's a female body there that is essentially the same as mine in the way it works, is an immediate turn off. If a transman lied about being trans and I somehow managed to not notice it either, it wouldn't make me bisexual. It would make them a liar.

Right but what if the "Transman' came clean and said she was a woman all along? Would you still stay with her? Because if so, yeah you would be a bisexual but you'd most likely fall into the Androphilic Bisexual since you're attracted to masculine presentation and sensibilities.