Gender is quite a fluid thing really, and can cover all kinds of factors as mentioned above. I believe most 'Ladyboys' actually identify as gay males, not females, but I suppose the argument could be extended to include transwomen as well as sexual attraction is mostly appearance-based.
Without getting into a complex gender debate, I think if someone looks like a woman, but is biologically male, it wouldn't make a man who found that individual attractive 'gay' (whether said individual identified as a man or a woman). The sexual attraction is towards a female body, not a male body. There are plenty of very convincing 'Ladyboys', and I'm sure most men who regard themselves as 100% straight would probably find some of them sexually attractive. It doesn't make them gay.
As for being with someone who looks female and identifies as male, it's probably a bit of a grey area. I don't think someone can be categorically placed into 'gay/straight/bi' based on that. I'm happy enough to let people decide what they are for themselves.