In that sense it honestly wouldn't bother me either way. At the end of the day I am female and always will be, even if my body looks more like that of a man these days. I get that sex plays a pretty key role in sexual attraction, at least for most people. As to how someone would identify themselves if they dated me, I guess it would depend on the person.
I have a few trans men who are open about it, though not necessarily immediately. They would find a straight women was attracted to them before they knew, and they would then have to disclose it to them. Normally that is followed by a bit of shock and people going away and thinking about it. Sometimes it's an immediate end to any attraction, but from what I've seen it's more often than not that people will find that their attraction hasn't gone away, which might be a big surprise to them. Whether dating a trans man would be right for them, regardless of their attraction, is another matter. But ultimately I think things often play out differently when someone has actually met a person and already developed that sense of attraction and connection, compared to how they would have expected to feel when considering it on a purely theoretical basis.
I also have a lesbian friend I know from college who was shocked to find herself attracted to a (biological) man she met in her late 20s. They are married with a baby now, so she doesn't really call herself a lesbian anymore. But she has said that she still sees herself as one because it's a big part of who she is, was her sole identity for such a long time, and he is still the only exception to her exclusive attraction to women. Bisexual didn't feel right to her in her situation, even though many would argue it is the accurate term. Sexuality is a pretty complicated in my experience, and I think a lot of people just use the word they think fits them best, even if it isn't a perfect description or if other people would disagree with that designation.
But for me, it wouldn't matter how they defined themselves in relation to me being trans, as long as they were a decent person and weren't only interested because they wanted to try something 'new' or experiment. Obviously people are entitled to experiment if they want to, but it isn't what I'm looking for personally. Practically though, it wouldn't be possible for me to both date a lesbian and remain stealth, especially as it wouldn't ever feel sit right to me to ask someone to hide their sexuality.