What is the way to solve the problem of a father and brother refusing a young man's marriage to a religious girl, fearing the authorities, and threatening him to shave his beard and their refusal of marriage according to the Sunnah?

Your family's view is pessimistic without justification, and the greatest possession a person has is their religion. Marry the religious woman, and establish your wedding upon goodness and religion, avoiding forbidden acts. If you fear, hold the wedding with only close relatives present, without a large celebration. Inform your father and brother that you are prepared to distance yourself if your presence with them causes harm, and do not fall into what is unlawful under the pretext of fearing something doubtful.