Is it permissible to abandon the act of growing a beard—which the questioner considers a religious ruling and is convinced of—in order to appease his brother who is not committed to the religion, especially if doing so might lead to conflict?

Your brother is not permitted to force you to shave your beard or shorten it. There is no obedience to him in this, because there is no obedience to a creature in disobedience to Allah. You must speak to him kindly, remind him of Allah, and explain to him the proofs for the obligation of letting the beard grow, and that this matter concerns you personally. Seek mediation from someone who can dissuade him from interfering with you in this regard.