What is the ruling on shaking hands with a male or female polytheist?

It is permissible to shake hands with a polytheist if both are males or both are females, or if the man is a mahram to the woman. As for a non-mahram (stranger), it is not permissible to shake hands with them, even if they are not polytheists. Some scholars have stated that it is disliked for a Muslim to shake hands with a disbeliever, but this opinion is not based on strong evidence.