Sure, and you could also say something along the lines of "How does that person identify?", "What is that person's gender?", or "What are that person's pronouns?". I should probably also add that gender identity is a VERY tense political issue in the United States, and I imagine that this is the case in other English-speaking countries, too...

I agree with Chris. Assuming that a persons pronouns are she or he, or that they identify as a man or a woman might might not be very polite, because they could be using different pronouns.