Toni Smothers was a ghostwriter for gotquestions.org for a few years this is one of her answers.

Question 36709: What does it mean to honor thy father and mother?

What if they are non-Christians? I know whoever does not leave their family to follow Christ will not enter heaven, but does this mean we should cut all ties?

There is a difference between obeying and honoring your parents. (Ephesians 6:1-3) To obey means to do as one is told; to honor means to respect and love. Children are not told in the Word to disobey God in order to obey their parents. Children are to obey their parents while they are still under parental care so long as they don’t demand something that would go against God’s Word. Adult parents are not required to be subservient to domineering parents.

The responsibility to honor parents is for life, however. God promises us His blessing for honoring them always. Children should honor their parents even if they are demanding and unfair. God’s blessing will be sufficient reward.

Cutting all ties with your family would only be hurtful. Praying daily for their changed hearts and eternal salvation would be much more productive and loving. Pray and be an example of Christ’s behavior and character for your parents to see. Live your faith out in front of them without jamming it down their throats or totally giving up on them.(Proverbs15:29, 1 Peter 5:3) Withholding your prayers is actually sinful. (I Samuel 12:23)

If we cut all ties with all the non-Christians in our life, who will we be telling the “good news” to? It is our great commission to spread the gospel to all the nations, not turn our backs on the lost of this world, especially our own family members.

Count yourself exceedingly blessed to be among God’s chosen. Simply out of gratitude, have no wish to glorify yourself or feel superior, (John 8:50), but be humble, (Ephesians 4:2), gentle and peace loving, (1 Timothy 3:3) do everything for the glory of God, (I Corinthians 10:31) and never alienate or stop praying for and loving your parents.