Amazing. I’m just listening to a shiur by Rabbi Frand. I will summarise here, even though it is a lot more complicated than this.
He said that the Torah tells us Terach died before Avrohom Ovinu left Charan, even though in reality he died only after. This is because we shouldn’t get the impression that Avram (as he was then) abandoned his elderly father. He really had an obligation to respect him, but was released from his obligation because of his commandment to go to Eretz Cenaan.
Anyway, what I understood from this regarding the OP, that one has an obligation to respect one’s father even if he is NOT Jewish.