Cultural practice is one of the lamest excuses ever invented to justify abhorent practices. If it's wrong, it's wrong, no matter how long the atrocity has been committed.
I think it depends. If the cultural practice is causing harm to other bodies, then I would agree. But something like "peyote trances" that Native American tribes have been using in ceremonies for generations, I think should fully be allowed. Right now in the US, as with most stuff the government can't understand or knows will actually cause the general population to think and expand their views, it is illegal to ingest peyote on a recreational and even sometimes religious basis. There are few organizations that are still allowed to use peyote in traditional religious ceremony in the United States (funny, since our country uses that "freedom of religion" in it's propaganda). In fact, I can think of only one organization off the top of my head: the Native American Church.
Taking peyote is a religious and personal experience. It should be up to the individual and as long as it does no harm to anyone else, there shouldn't be a problem.
But if the cultural practice is stabbing animals to death, cutting off fins, or sacrificing babies, then yes, I think we and the particular culture in question should take a step back and look at what we/they are doing.