Does the mitzvah of Kibbud Av Va’em apply if one’s father is not Jewish?
What about giving the proper kavod to a Jewish parent, who is openly hostile to religion? Is it permissible to argue with them le’shem Shamayim?
Although the formal obligation of honoring parents does not apply to a non-Jewish parent, and there is no penalty for hitting them, one must honor a non-Jewish parent, in the way that even non-Jewish children honor their parents. This halachah is ruled for those who convert to Judaism, who must still honor their non-Jewish parents, in order that the non-Jews should not think that Judaism is less moral than other religions.
If the parent is a rasha (wicked), authorities (Rambam and Tur) dispute whether or not there remains an obligation to honor them (see also Aruch Hashulchan, Yoreh De’ah 240:33). You should honor the parent, but it is certainly permitted to argue with them about issues of religion, and perhaps they will one day be convinced.