Q. Is my rabbi right in not shaking hands with women?
A. Physical contact with women is a halachic problem, even with one’s own wife when she is niddah. Many authorities rule against shaking hands with women if there could be any sexual or erotic interest involved. It could be different in a business context where a commercial transaction is being sealed (Shulchan Aruch, Even HaEzer 21:5; R’ma’s glosses).
The Bach, commenting on the halachic issue, says that “In our country people are lenient in these matters and we do not forbid it”, provided the handshake is perfunctory and L’shem shamayim (“for the sake of Heaven”). An illustration is given from Talmud Yerushalmi Sotah 3:1 that a kohen was allowed a brief contact with a woman’s hand when she brought a meal offering. Since the touching of her hand was brief and utilitarian there was no thought of sexual desire.
Those rabbis who shake hands with women do so because it is a mere social convention without any deeper implications. Other rabbis avoid any physical contact, though some will shake a woman’s hand if she puts out her hand first.