Most unpopular beliefs are false. However, if everyone subscribed to strict majoritarianism and never took up unpopular beliefs, intellectual progress would cease completely. There must come a point at which cost we pay in wasted effort because of false unpopular beliefs is worth the payoff in progress through new ideas, which of course all start off unpopular. So while I'd like 9-11 truthers to see the error of their beliefs, I'd like to achieve that through argument based on fact, rather than through simply pointing out that everyone disagrees with them.

Also, of course, strict majoritarianism is self-defeating, since it's a pretty unpopular stance in itself.