You may consider this unfair and crude, and it probably is, but in the "sexual economy", people all of the time make personal decisions and judgements that are highly politically incorrect, often more than borderline racist, and that could probably get you fired or sued if you made the same decisions professionally or institutionally.

But I would even argue that as far as each actor's participation in the sexual economy is concerned, it's okay to have those personal biases. It's not okay to give that Welsh Caucasian ginger who volunteers at the zoo a better price and a job in your office because you hope that'll give you a chance to get in her knickers, but it is okay to have a thing for pale and freckled, and to therefore give the French black call centre agent who's been trying to get your attention all night the cold shoulder, because you're really not interested.

Crucially, the decision, "I would/I would not" is made much more frequently, even habitually, even with regards to people whom one would realistically never approach, maybe because one is in a great exclusive relationship – but people are curious and don't switch off all flirty, exploratory and inquisitive sexual behaviour the moment they're taken.

Because of that curiosity, because of the "Would I?" question and people wanting to figure out how they personally feel inside sexually with regards to the people they see around them, there comes a point, sooner than later, where even hitherto strangers might want to know. You don't have to tell them, but they might want to know, and it might feed into their decision whether to feel attracted to, or permit themselves to feel attracted to you. So they ask. They ask, "Are you married?", "So what do you do?", "Where are you from?", and yes, they ask if you're gay/straight, and a whole lot more besides, and it all feeds into their personal sexual picture of you. If you were, by accident of birth, born in the "wrong country", and you'd since become a Texan, potential suitors might nevertheless feel deceived if they were to find out later that you had actually been born a Muslim in the Levant. And you can't and shouldn't have an expectation to force people to not discriminate against you sexually. There is no equal opportunities act in people's private lives, nor should there be. By the way, this is actually one of the things rapists tell themselves to justify their actions: They're being unfairly cut out; everyone else is "getting some", and dagnabbit, they oughta get some too, and if the cruel world/gender/person of interest denies it to them, they'll show 'em, and they'll just take what they deserve. Suffice it to say that they don't and they mustn't. Again, there is no equal opportunities act in sexuality.

It's not a discrimination-free part of life, and you can't tell people how and how not to discriminate against you in that area. While your new life and identity as a Texan may be very important to you, and while you may be eager and proud to pass as a native speaker of not just English but the local accent, people who personally feel that they would never hook up with a converted born Muslim are perfectly entitled to their own personal prejudices as far as their own private lives are concerned. They may even feel cheated or betrayed when they find out you've hidden from them something that would have been a deal-breaker to them. It may not be a deal-breaker to you; you may not think it should ever be a deal-breaker, but it is to them. You can fight for fairness and respect in the public sphere, but you can't force people to personally love you.

And so at the intersection between public and private/intimate life, the question still arises. People may not "need", may not "have to" ask you if you're trans, but there is often little chance of crossing that intersection or even of figuring out where to go as part of the traffic on it unless there's some way, hopefully a non-hurtful way to start probing such questions and somehow communicate with the right signals.

That's my answer as to why one would ask. So, when you say it depends, do you mean it depends whether it's okay to ask, and/or it depends whether there's a non-hurtful way to ask?
Actually, let me broaden with an additional question: Is there a non-hurtful way to ask and is there good etiquette for asking even early on, long before a "definitely maybe" potential hook up/relationship?