We all know that the Bible commands, "Honor your father and your mother" (Exo 20:12). In fact, Paul points to this one in the New Testament to urge children to obey their parents (Eph 6:1-3), which would certainly indicate that this command is still in effect in the New Covenant. Of course, almost immediately the objections come out. "Well, sure, when you're a kid, but not after you grow up and leave the house!" Or, "Oh, yeah? What if they're lousy parents?" And so it goes.
The question is worth examining because, as it turns out, we're told to honor other people that aren't always so ... honorable. Take, for instance, the command in Peter's epistle to "Honor everyone. Love the brotherhood. Fear God. Honor the emperor." (1 Peter 2:17) You have to ask, "Hey, wait! Everyone? And especially the 'emperor'?? I mean, what if the emperor is a devil?" Surely God wouldn't require a believer to honor, say, Hitler? Right? Well, remember, Peter was writing under the Roman Empire and the "emperor" that he was thinking about specifically when he wrote this was ... shall we say, not a good emperor. Remember, they date Peter's death as somewhere around 64 AD during Nero's reign. Talk about an evil emperor! When Peter told them to "Honor the emperor," he was clearly not saying "Honor good emperors (like Nero?) but don't bother honoring bad ones." So a good emperor or good parents or good people ("Honor everyone") are not in view here.
I would suggest, then, that we might need to revisit "honor". What does that mean? If it does not require people to be good in order to honor them, what does it mean?
The English word means "to regard with respect". Honoring an obligation, then, would be to respect it sufficiently to fulfill it. But in terms of human interaction, it means simply to show respect. Interestingly, this is not the meaning of the original Greek word. At least, not in its literal sense. The word used both by Peter and Paul is τιμάω -- timaō -- which is a reference to value. It means to fix value on, to prize. That is respect, sure, but it isn't mere "admiration" as we use "respect" these days. It is assigning value. Note that the value is assigned. It isn't necessarily intrinsic. Thus, biblical "honor" is ascribing to something a valuation. It is to prize something. Or rather, in the cases we're looking at, to prize someone.
Now, let's not get confused. First, "honor" may be or may not be the same as "obey". It may not require agreement. It may not include enabling. Let's consider a less volatile example than Hitler or that drunk father. Let's say that you have a pet that you value. That pet gets sick. That pet hates going to the vet. So, out of consideration, valuation, honor, you do not take that pet to the vet, right? Because, after all, she hates going to the vet. No! If you value your pet, you will violate her wishes and take her to where the best care can be given. You see, then, that honoring a pet or a person may not include going along with them, agreeing with them, enabling them, or even obeying them. What it will involve in all cases is seeking their best interests, even when they don't agree.
In this sense, then, you might be able to step back again to the question at hand and see that it could be possible to honor your mother and father even if they are bad parents. It would be possible for a wife to respect her husband (Eph 5:33) and, when he refuses to seek help for his drug addiction, turn him in to the proper authorities to try to take care of that problem. Peter, for instance, were he commanded by the emperor to profess him as God, would be obligated out of respect and honor to decline. It would not be in the best interest of the emperor to try to retain that position, so it would not be honoring to the emperor to acquiesce to such a command. As Peter said and demonstrated in Acts, "We must obey God rather than men." (Acts 5:29) To do otherwise is not honoring to parents or emperors or even presidents.
Now, I realize that there are those who would choose to disagree. I realize that some will say, "Oh, no, you do not honor an emperor if he is like Hitler. You do not honor parents who do not earn your respect." I know. I also know that the Bible disagrees. And I know that moving the absolutes like "honor your father and your mother" and "honor the emperor" to "if you think it is wise" is placing God's commands under our approval. At this point, we are merely asking, "What is the threshold at which I can discard a command of God?" Call that what you will; you cannot consider it wise.