Yeesh, well that's a bad situation to be in.
To answer your question requires a fair bit of detail on situations posters will be familiar with and it's likely to not be a pleasant read, so this is an advance warning.
Suddenly being confronted with that question would be triggering the hell out of my existing fight or flight trauma responses and make me want to get the hell out of that situation ASAP in order to escape potential harm, so I'd be looking for the quickest safe exit that would protect me from disclosure and the potentially life-ruining implications it would hold.
If it came out of nowhere I can't say with any certainty if I'd be able to keep a cool head and gracefully find a safe way out without revealing how frightened the question had made me - a dangerous thing to reveal. It would depend on the wider context and what else I knew about the person in question, ultimately - I've had a lot of experience dealing with men like this over the years, unfortunately.
If I was alone in a remote place with this guy, especially without my own means of transportation, there would be a very real danger that disclosure could be life-threateningly dangerous. I couldn't trust that the man in question, having already hinted at holding negative opinions about trans people, would be likely to have much better views about women and consent in general - so even just firmly withdrawing consent in this context and asking to go home is already dangerous.
If I'm thinking quickly and it seems safe, I might try to respond with something along the lines of "That's an odd question - would it make a difference to you? I'm a feminist, by the way, and I have no interest in dating transphobes so I'm not sure this is going to work out. Let's save ourselves both a lot of time here."
Hopefully, if he isn't a creep, he'd take it as an opportunity to reflect on his own ideology - he's likely to meet plenty of other feminists in his life and this is going to be a common response.
If I was getting a sense that he was using it as a hypothetical question to confirm I shared his secret anti-trans views, and only the transness part would be the dangerous bit, I might instead try an angle of 'absolutely not and as a gender critical feminist I find the notion offensive, please apologise immediately' - it's a dangerous gambit but we're already in a dangerous situation and it might be enough to buy time and escape the immediate threat.
If the vibes are so bad that it's clearly not safe to even challenge him at all, then we're already into nightmare crisis survival mode. The only safe course at that point is to do or say nothing that could make the situation worse. I certainly wouldn't reveal I was trans at that moment.
I've had surgery, I never developed adult male muscle mass and strength and my appearance doesn't give any indication that I am trans, so at this point I'm effectively in the same situation any other non-trans woman is when having to find a safe way to communicate a lack of consent and escape danger after you've just discovered your partner is probably a hostile bigot and you don't want to stick around to find out.
The priority would be de-escalating the immediate situation and bringing him back 'on side'. A long, long time ago I used to have success with absurd humour or sarcastic deflection (a comically overblown and unambiguously OTT mock-confession like 'oh my god my terrible secret is out! All this time I have actually been Dave the Deceiver!') to break the tension and humanise myself in his eyes while creating the impression that it isn't a big deal; we're friends and can have a laugh about it, right?
In my unfortunately quite extensive experience, fragile men like this are often deeply insecure, deeply homophobic and terrified of being humiliated or made to look foolish, so the key thing would be to never make them feel powerless while assuring them that their masculinity (and heterosexuality) isn't in any way threatened.
De-escalate; disengage but don't do so suspiciously. We're chill people having a nice chill date. Nothing is harmed; nothing is threatened. His manhood and pride remain safely intact.
As soon as there's a suitable exit, take it and never ever engage again.
The reality of course is that it's incredibly difficult to Poker Face your way through these situations and fragile men get very unstable when their insecurity triggers. It's all very well having an idea of what you probably should do, but fear, proximity and context can throw that all out of the window.
It is not a situation I would ever want to get close to being in if possible, but I have been in similar ones quite a few times when I was younger unfortunately.
That was a rotten place to revisit. Not particularly interested in going there again, so thanks for the question I guess and I hope the answer was helpful but I'm really not interested in spending any more time on it.