There is nothing inherent about a republic that protects the minority from the majority. What does that is the Constitution's limitation on federal powers and the amendments providing for individual rights (and Supreme Court decisions that decided that the protection of our individual rights apply both against the federal government and the state governments--that's nowhere in the Constitution...silly judicial activism). A republic just means a representative democracy, i.e., all the people don't vote on everything, instead we elect people to vote for us. Republics like ours are democracies, just not "pure democracies" in the sense of we all vote on everything. However, as noted, we do have purely democratic features in many states and localities, i.e. voting on propositions.
I go back to something I said here many pages back: I belivee in electing someone that I trust to represent my interests--even if I don't agree with them on all important issues--is more important that voting for someone who I don't trust, but aligns very closely with my political opinions.
