I'm going to say no. Certainly people have the right to their cultures and, if you're talking about separate, sovereign nations, we should butt our noses out but just because I'm not trying to change someone, doesn't mean I have to respect them either. There are practices in many parts of the world that I, as a modern American, find barbaric and horrid, and would never allow to be perpetuated on me or mine, but for the people who live there that is the way life is and trying to tell them it's wrong is baffling to them. I don't have to like or respect it, but I don't have the right to try and change it either, only the people living it really have that right.
Now talking culture on the smaller levels you mentioned (gangs, teens etc.) that happen within each country; some should be respected, others not so much. I have no respect for gang cultures. These are groups that are, most often, carry out a series of illegal activities and harm so many people in so many ways (including the gang members themselves who end up dead or in jail) it's probably hard to truly quantify. If there were a good way to stamp this out without causing even more mayhem I'd be all for it.
Smaller sub-cultures that are non-violent and non-harmful (such as the Amish or collectives of people from the same area originally trying to keep parts of their original culture alive, "Chinatown", "Little Italy" etc.) should certainly be respected and even learned from. Calling Teens as a whole a culture is a bit hard because they don't really have a cohesive sort of core. I tend to see them more as people still looking to determine what sort of culture they are wanting to be a part of, learning and making choices, but not quite finished yet. They shouldn't be marginalized, these are HARD choices to make but I don't see them as having their own, distinct, culture so much.
Oh any any respect I might have for another culture, just like for another person, ends if the safety of my family, or myself, is threatened.