The Shu”t Mishneh Halachos (4:186) discusses if the issur of touching and looking at women applies to both Jews and non-Jews alike, or if perhaps it applies to just Jewish women. He writes: According to the Rambam who learns the issur from לא תקרבו, it would seem that by non-Jewish women there is no de’O’raisa, as by non-Jews only derech chasnus [way of marriage] is a problem, and it may not even be derabanan. See inside where he speaks about this at length.
He then says: If this assumption is correct, there is more room for leniency (at least in America), as most people traveling on the subway are not Jewish, therefore, there are lots of doubt involved: Who says one will touch the women; even if one does it’s done unintentionally; even if one bumps into a woman, she may not be Jewish.
Then he says: Yidden have always been traveling from place to place, both men and women, and people weren’t particular. Our generation is certainly not better than previous ones, therefore, leave Klal Yisroel to do what they do, and don’t start saying it’s forbidden. However, certainly, if it can be avoided one should avoid it.
