Thanks for your question.
The commandment to "honour your father and mother" is a very important and very high on God's list of priorities. See Exodus 20:12; Deuteronomy 5:15; Matthew 15:4; 19:19; Mark 7:10; 16:9 and Ephesians 6:2. It is interesting to note that Paul is writing in Ephesians 6 to many who were gentile converts to Christianity, many of whom, would have had unbelieving parents.
So long as one's parents do not make ungodly demands on their believing children, they must obey the divine commandment to honour them. However, if giving such honour and obedience will lead one into sin, one has a higher duty to God. As Peter said to the Jewish court who tried to forbid him to preach the Gospel, "We ought to obey God rather than men." [see Acts 4:19; 5:29]
I hope you have found this helpful.