By translating to "familiar to me" instead of "familiar with me" does this sentence indicate that the speaker knows the women, but we don't know whether the women know the speaker? Or does it imply mutual familiarity? If the former, how would you say "the women are familiar with me"?
I have heard if you go to a "cà phê ôm" the women could try to be familiar "with" you.
Somehow "familiar with" conveys, at times, a sense of personal closeness, as in, "Don't try to be familiar with me." Perhaps this comes from the root meaning of the word in "family." The idea of "having some knowledge of" is, after all, derivative.