benignuman: The mainstream position, by far, is like the Chazon Ish and the Steipler. Which is how mik5 correctly explained it. Rav Moshe, in the Igros Moshe, repeatedly in multiple teshuvos (EH I #5, OC I 113, EH IV 32.9) says it is impermissible to shake a woman’s hand. Even if she sticks it out. And Rav Moshe specifically paskens that claiming there is no chiba is unjustifiable.
Please cite any first-rate posek who disagrees with this strong position of the Chazon Ish, the Steipler and Rav Moshe amongst many others.
The Chazon Ish stated [re: a man shaking a woman’s hand who is not his spouse, his mother, his daughter, or his granddaughter] [p.p. 130-131])
A Yeshiva student from England refused to shake hands with his step-mother when greeting her. His father was extremely upset with his refusal. He demanded his son display “derech eretz” towards his step-mother and shake her hand. The son refused stating he was taught it was impermissable with a non close blood relative. This affected the fathers relationship with the son. Some family members told the son to give in al sholom bayis. The son asked a shaila from the Chazon Ish. The Chazon Ish responded with a short and sharp answer – “Chok V’lo Yaavor, Issur Gamur” (It is a prohibition that one dare not violate; It is absolutely forbidden,) Violating this halacha was out of the question despite sholom bayis and kibud av.
Its also paskened assur in Responsa Be’er Moshe 4:130, and the Od Yosef Chai (by the Gaon Ben Ish Chai zt’l) Shoftim #22 where they rule it is totally assur. The Sefer Chassidim # 1090 writes one should not shake hands even if the person of the opposite gender is not Jewish.