Well as you're seeing with gay marriage bans being overturned, just because the majority want to strip the minority of their rights, they shouldn't be allowed to.
I know that. It was a general point. In a pure democracy, 51% has complet power.
Also while the US is a formal republic, it does often emulate a democracy. Based on common belives the constitution is reinterpreted, or simply ignored. This has been well documented by legal scholars such as Richard Epstein.