If you find a group of people who say they have pain and have behavioral and neurological correlates consistent with some sort of pain, that's usually good enough. You try to find a way to alleviate their pain.

If you find someone who says they are hungry had they have behavioral and possibly neurological correlates with hunger, usually that's good enough too. You get them some food.

People who are gender dysphoric say they are, and have behavioral and in some cases neurological correlates consistent with this, so wouldn't that also be good enough? Yes, there may be other populations who identify as trans for whom the parallel is less clear, but you seemed to be doubting the clearest cases too, where for other subjective matters we would always presume that the account is forthright rather than deceptive.

The problem of other minds doesn't seem any easier or harder here than for anything else. Clear cases are clear, though mistakes are possible. There may be less-than-clear cases also, but you handle those the same way that you always handle not having direct access to mental states: if there is reason to doubt, you look for correlates.