I've only socialized in gay or straight space, I've never been to a trans space so I can only offer some thoughts about people who aren't necessarily sensitive, and generally end up asking too many personal questions.
Background: I pass very well I'm gay and socialize in gay only spaces frequently. I'm not out. Most people, even a lot of my closer friends, don't know that I'm trans. So it really only comes up if I'm interested in somebody.
So the best advice I can give follows: Be yourself, don't be too guarded, (this can be hard because more often then not it seems I'm the one with the issue about having a trans status, not them) don't be too uptight, have fun, let your you shine and see what comes of it. If nothing, oh well, you're not off any worse than before. I've found it's rare that the whole trans thing becomes a deterrent.
If it turns out I do like them enough, I just suck it up and tell them, if I'm truly interested then it's something they need to know. If I don't do it then clearly my interest isn't strong enough. This generally takes a long time, and is almost always more angst than it's worth.
Though I'll admit I've used it as an out in an attempt to lose interest from a guy I'm not interested in, if I feel bad about not returning the feelings. This has never actually worked.
Over all I've only had two people say it's an issue or lose dating interest. In my experience most gay men really just don't care if they see a boy and become attracted to a boy. This is particularly true if they want to date you.
For purely physical interests, or something similar, I've found it to be about 70/40. Most don't care, many think it's a bonus, a few will tell you it isn't their thing.
Overall it seems I get more worried about my status than my gay/friends/lovers/boyfriends ever were. For all the gross comments made on comedies and sitcoms about trans folks, most people, particularly if you know them a while before disclosing, are very accepting.
I have no idea if this is true with women, but I'm willing to bet it is.