The question is unclear as to what is meant by “two different ways.” Does it mean two different preferences of living or two different religions?
First what does it mean to have different preferences, and how can we honor our parents? Does it mean we agree with them on everything? What is the guide we should use?
Honoring your parents would be to show consideration, respect, care, attention and appreciation for the good for they have done. You can show appreciation, consideration and care without necessarily agreeing with them. If you are an adult and live at home with them, it would be appropriate to follow their guidelines and rules (as far as conscience would permit). “Follow peace with all men and holiness without which no man shall see the Lord..” (Hebrews 12:14) We all need to give a little to make a household run smoothly. If you have your own residence follow their preferences at their home and do what you like best at your home. That’s part of the privilege of adulthood – setting up a household the way we would like.
Sometimes parents can be selfish or unreasonable. What should be done then? We can’t let demanding parents control our lives. If there is a degree of selfishness, inevitably it will affect the degree of respect. Even though that may be true, still show as much respect as you can. Remember, your parents brought you into this world. Always try to have the motivation of love.
What if parents attend two different Christian denominations, or one is Christian and one is non-Christian? Honoring your Heavenly Father would need to come first. At times, this may conflict with those we love. Matthew 10:34-37, “Think not that I am come to send peace on earth: I came not to send peace, but a sword. For I am come to set a man at variance against his father, and the daughter against her mother, and the daughter in law against her mother in law. And a man's foes shall be they of his own household. He that loveth father or mother more than me is not worthy of me: and he that loveth son or daughter more than me is not worthy of me.” Our touchstone is always the scriptures.
In Summary: The deciding question should be – what will please and honor our Heavenly Father? But when we disagree with each other, we should always be kind.