R’ Schachter might in theory agree with Charlie, but he adds an important caveat. The Gemara calls it an Ervah. So he says a Jewish woman should be as uncomfortable singing in front of non-Jewish men as she would be standing untznius* in front of them (of which there might technically be no Issur either, but the vast majority of Frum women would obviously, and correctly, be very uncomfortable doing so).
*Edited – Sam means as untznius as possible.