This is a great question because it focuses on two words that appear in the same verse in the Bible, both relating to our parents: obey and honor. The verse is Ephesians 6:1, and it goes like this:

"Children, obey your parents in the Lord, for this is right. 'Honor your father and mother'--which is the first commandment with a promise--that it may go well with you and that you may enjoy a long life on the earth."

Now, the first impulse might be to put "obey" and "honor" in the same category, but that isn't what the apostle Paul is after here. First, on the matter of obedience, this applies to children when they are under their parents' authority and care. Second, children are not commanded to obey their parents if it means disobeying God. An example of this would be if a parent asked a child to steal something (don't laugh, it happens). If the child knew better (maybe the child has been to Sunday School and learned that stealing is wrong, or perhaps the child just nows it's wrong to steal), then it would be wrong to steal even if it meant "obeying" a parent.

In either case, an adult is not obligated to obey a parent in the same way a child is, and an adult child is not obligated to be in subjection to a domineering parent. An example of a domineering parent is the one you gave: a parent who demands that an adult child agree with them on a certain topic of the Bible.

Now, on the matter of honor, this is an entirely different issue, and Paul makes it clear that honoring our father and mother is a command. To obey means to do as you are told. By contrast, to honor means to respect and love, and by love, the Scripture means unconditional love. Even if the parent is domineering or wrong, we are to love and respect. In the case you are citing, it would be entirely appropriate for you to say to your parents on a particular area of disagreement, "Mom and Dad, I love you, but I must respectfully disagree, and let me explain why." To dishonor would be to say something like, "Mom and Dad, you are so wrong. I can't believe that you take that view!" Even if your parents come at you with that tone, as a child, your responsibility is to love and respect them.

I have a friend who has helped millions of people deal with difficult family situations through his books and seminars (if I gave you his name, you would know him). His own father abused him throughout his life (verbally, not physically), and it was not until his father was dying that my friend was able to "make peace." Never throughout his life did he dishonor his father. Now, when he talks to others about his relationship, he is able to honor his father.

Hope this helps put the matter of "obey" and "honor" in perspective.