We wrote about this in our border search guide and concluded that there is a risk of being refused admission to the U.S. in this case (in the border search context) because the CBP agents performing the inspection have extremely broad discretion on "admissibility" of non-citizens and non-permanent residents, and refusing to cooperate with what they see as a part of the inspection could be something that would lead them to turn someone away. (However, this is still not quite the same as forcing someone to answer in the sense that they don't obviously get to impose penal sanctions on people for saying no.)