Is it permissible to pray behind an Imam who repeats his prayer after finishing it due to obsessive doubts (waswasah)?

Your following your father, who suffers from waswas (obsessive doubts), is valid and permissible, and there is no harm in it. There is a difference of opinion as to whether or not it is disliked for him to lead you in prayer. You should advise him by explaining the danger of waswas, the necessity of avoiding it, and that he should not repeat the prayer after finishing it, because by doing so, he commits what the Prophet, peace and blessings be upon him, forbade, which is repeating the prayer twice.