Yes. If you consider someone to be your BEST friend, then you should stick by them no matter what. If they're wrong, help them see that they are and then help them through whatever it is that they're going through.
As for your drug reference, that is pretty darn low, in my opinion. I mean no personal offense, but if your friend had started taking drugs, do you honestly think that the best thing for you to do would be to walk away from them when they obviously need you to tell them to stop? You have your own will, just like every other human being, and only the weak-willed ones are the ones who get pressured into doing anything. Be strong for yourself and be strong for your friend.
Personally, I would NEVER leave my best friend hanging, no matter how stubborn or wrong she is/may be. We've been through hell and back together, and through everything she's helped ME with, I think she deserves the same kind of respect from me. You have to ask yourself this, if you were in trouble, or in the wrong, would you want YOUR best friend to walk away from you because they didn't want to get into anything?
Best friends should stick together through thick and then. Correct me if I'm wrong, but I thought that was the point of having a BEST friend. You can go to them with anything, talk to them about anything, and lean on them when you're in trouble. You can also expect them to smack you upside the head when you're doing something stupid, too. This should go both ways, for it to be a true best friendship.