It is rude to ask someone if they're transgender?

It depends on the circumstances but more often than not it would not be rude as such but come across as slightly offensive.

Well, if you just walk up to someone and ask them out of nowhere, then yea, I think it is, but if you know the person, or if you've talked to them for a while, then I don't think so.

Forgive me if you feel this is unfair, but is it rude for someone to ask you about your genitals? That's basically what you're asking there.

Yes, it is rude. If they want you to know they'll tell you.

The obvious exception is if you're giving them medical help and the information is necessary.

Its not rude but that is just in my book.

Yet in the end why would you want to know. If the person wanted to tell you they would have already done so.

It might be, if you don't know them. If you're an acquaintance of him/her, you might be able to casually bring it up with a lead-up conversation.