You know... my (admittedly limited) experience with this sort of thing has been that people who have not had to deal with their own gender identity & / or sexual orientation issues just really don't have a clue what it's all about. And, for the most part, they really don't care either. I obviously don't know why your partner's mom would ask if you are trangender… ideal curiosity perhaps?
From my perspective, you're absolutely right. It's just downright rude to out someone without their permission. I think just saying one doesn't know enough about it to answer the question would be a good way to respond. Or in the alternative a person could perhaps say it's a personal matter & not something that's an appropriate topic for discussion.
As far as how to approach this, or if it's justified, my personal opinion would be that it is absolutely appropriate to bring up. This is your partner who did this & left you feeling violated. It's important to air your concerns out & not ruminate over them. If it was a casual friend, someone you don't see that often or care that much about anyway, maybe it would make sense to just let it go. But not in this case I don't believe.
On the other hand, as I wrote at the beginning of my reply, I don't think most people have any more than a cursory understanding of gender identity or sexual orientation. And I suspect, in most cases, they don't really care either. So I think, while you do want to air this out, you also want to tread lightly as much as is possible. Exactly how you go about doing that is something I can't say. If your partner is a person who takes offense easily, it may be tough. But I do think it's important to at least mention that how this was handled hurt you. I wish you well...