What is the ruling on the action of a father who refuses his son's marriage to a committed girl and stipulates that she shake hands with non-mahram men before the marriage contract, justifying that by fearing for his son from excessive commitment?

You must try to convince your father to dissuade him from his religiously forbidden request, as it is impermissible for a woman to shake hands with those who are not her mahram, and there is no obedience to a creature in disobedience to the Creator. If he does not respond, then it is permissible to marry her without his permission due to his stubbornness and his stipulating what is impermissible, and because of the praiseworthy qualities she possesses.