I would have had your same concerns. I always have my guests tell me a little about themselves and the people traveling with them. If I get no answer, I let the request “expire” because requested info was not provided. If I get vague answers, in a friendly tone I ask a couple of questions asking them to clarify. After that, if I am at all uncomfortable with the exchange, I do not accept the booking.
Denying a booking request won’t hurt you, unless you do it regularly. Too many rejections can affect your placement in Airbnb’s search algorithms, and you might get nastygram email warnings from Airbnb.
I want polite, appreciative guests in my properties. I’m not aware of any discrimination laws protecting rude, entitled guests, so as long as you comply with the protective laws of your jurisdiction, you don’t have to worry about that.