Assuming that the majority who wants to stomp on some odd minority has more love for the law than their fellow man? Otherwise, what is keeping them from doing as they please? Also, "republic" is a vague term, and I have no idea why so many folks have started using it to refer to constitutional democracies, except maybe to advocate that the democracy be taken out of constitutional democracies, and tradition made king.
This goes back to Aristotle, who made a difference between the three possible forms of government: 1. One governs (monarchy), 2. few govern (oligarchy) or 3. all govern (democracy). According to him, a democracy inevitably becomes a tyranny.
And that is what all enlightened philosophers based their thoughts on. They all agreed a republic is the best form of government, where all three archetypes of governemnt are mixed: One governs (President or Prime Minister), few govern (members of parliament) and all govern (representatives are elected by the people). Throw in Locke's and Montesquieu's idea of separation of the branches, Rousseau's sovereignty of the people, and you got a modern republic.
"Republic" is the original term for modern "constitutional democracies". Those who keep calling it "democracy" are those who use the wrong term, since they don't know the basics of state philosophy.