What should a son do who promised a girl marriage, while his parents refuse this marriage because they are uncomfortable with the girl's parents and did not choose her themselves?

Obedience to parents and showing them kindness are obligatory. However, their obedience is limited to what is good and does not involve disobedience to Allah the Almighty, and to what benefits them without harming the child. If their abstention from a certain matter does not benefit them, or if it harms the child, then obedience to them is not obligatory in that instance.