It can be summed up in two words: be careful, and please try to warn before you ask about really intimate stuff. Genitalia and trans, for example, being "really intimate stuff".
There's a background to this, obviously; I got a nice, yummy cystitis the other day (die e. coli, die) and had to see a doctor. My usual GP wasn't around (bless him, he needs his vacations, too), and so I took the first doctor I could get. Now, as I'm sure y'all know, cystitis means an infection is having a party in your urethra, you need to pee like mad and it stings and it's all very nasty, really. You need to see a doctor. DIY-ing is not an option, even though cranberry juice can help. You don't want any nasties in your urethra, and you definitely don't want them in your kidneys. And also, you having a trans background, it might be it's got something to do with surgeries - not very likely if it's been years and years, but it might; and the doctor sure as hell won't know, unless you 'fess up.
Trouble is, I hate explaining my background to people. It's a vile affair, and there's no way to make it comfortable to me. So. When the doctor asks me (he's very polite and affable and all) if I'm on any meds, I tell him I'm on HRT. I take a calculated emotional risk. He proceeds to ask the specific meds (I start getting uneasy at this point because I can tell where this is headed, right there, right then) - I tell, and start cursing silently to myself for telling. He then proceeds to ask me if this is because of trans. Which feels just about horrible, and I feel like I've been stripped naked against my will. I fumble on about it, get the prescription for an antibiotic (well duh, an UTI is an UTI, and my symptoms fit the description to a T).
Afterwards, I feel violated. Yes, I know, I'm sensitive, but blow me, I am. And I don't feel that's really to be faulted; I've had to explain this trans stuff against my will to a number of doctors in order to get the treatment I needed. It's one pact with the devil - yeah, you get the treatment you desperately need, but the price is that you need to play by their rules, and the rules for women brand you as trans: slightly off-the-rocker, pathetic/deceiving (take your pick, girl!) mental case. This seems to be considered as a permanent feature, even when you've gotten all the treatment you wanted and no longer fit the diagnostic criteria.
I took up this experience (it wasn't an experience from hell, but it was nasty - I'm not used to being identified as trans without my prior consent; the last time it's happened must've been, I dunno, like a decade ago. Yes, I'm one lucky, and healthy, bitch.) with him later that day, and sent him an e-mail describing my experience of the visit. He called back, explained stuff and, well, he's ok in my books now.
In retrospect, what I think he could've done differently is at least give me a warning he's going to ask me an extremely personal question. That might've given me some time and mental space to prepare myself. My rationale for this is that there's really no universal solution to asking about genital configuration; while I'm able to produce more-or-less precise information on mine, I'm pretty sure most people aren't. A question about genital configuration would simply be unintelligible to them, and asking, point blank, if you've got a penis, a vulva or something else is potentially just as invasive (or maybe even more) than asking someone about trans. I would prefer such questions, but I'm pretty sure many more people couldn't take it. And there's no way for the doctor to tell as far as I understand it.