Can I shake hands with the opposite gender?

“If you are referring to shaking your mother in law's hands, then it is permissible as she is your mahram. However, on account of the abundant fitnah prevalent nowadays, it is better for the mother in law and son in law or father in law and daughter in law not to shake hands or hug, but merely make salaam verbally.”

“It is not permissible for a male to shake hands with a non-Mahram female and vice versa. Rasulullah (Sallallahu Alaihi Wasallam) has prohibited this and condemned this with very strong words:”

“To greet and make Musaafahah (shake hands with each other) is established from Rasulullah Salallahu Alaihi Wasallam. In fact, Hadrat Abu Zarr Radiallahu Anhu was asked, “Would Rasulullah Salallahu Alaihi Wasallam shake hands with you (the Sahaabah) when you met him?” He replied, “Every time I met him, he shook hands with me.””

“Handshaking when greeting a person is termed ‘Muṣāfaḥah’. It is Sunnah to make Muṣāfaḥah when greeting a person.”