Is it permissible for this young man to shake hands with non-mahram women, knowing that his mother threatens not to speak to him if he does not do so, and he is at the beginning of his commitment to the correct creed, and his parents and uncle are Sufis, as are most of the people in his village?

Evidence for the prohibition of a man shaking hands with a non-mahram (definition) woman has been previously presented. Therefore, a young man must avoid shaking hands with non-mahram women. He owes no obedience to his mother or anyone else in this matter, for obedience to a created being is not permissible when it involves disobedience to the Creator. He should be gentle with his mother and explain the truth to her with kindness and respect, while striving to treat her well and pray for her, for honoring one's parents is among the greatest obligations.