"It's not the only discriminator, but it is the basis for the legitimacy of the government, per the Declaration of Independence, and incorporated in the Constitution."
The entire purpose of the constitution is to protect the freedom of the individual from the political whims of the majority.
"Democracy is not freedom. Democracy is two wolves and a lamb voting on what to eat for lunch. Freedom comes from the recognition of certain rights which may not be taken, not even by a 99% vote."
In other versions there is a note about "liberty being a well-armed sheep contesting the vote."
"It doesn't mean that minority rights override majority rights whenever they disagree."
If the Supreme Court were to strike down the minimum wage law, exactly whose rights would be getting violated? By not having a minimum wage law, you are not imposing on anyone. By having a minimum wage law, you are. So you're argument only works if your starting position is that one person has the right to abrogate another's right.
"In a more general realm, if governmental decisions are not made based on a majority vote, what should they be based on?"
It's totally dependent on the situation. But a rule of thumb is that the political desires of one person or persons should never be considered sufficient to override the individual freedom of another. I like inequality. It is an indicator of just how free you are. Consider a bar. You go to any bar where young men hang out. 80% of them will go home without a girl. 10% will go home with a girl, as they randomly do. A much smaller number will go home with a different girl this night than he did the night before. That's inequality. It occurs because each of us has certain characteristics that make us more valuable or desirable. It's a function of who we are. And just like you wouldn't force the most attractive women and men to have sex with people they otherwise wouldn't, you don't force people to pay a wage higher they willing would.
Inequality in the eyes of the law-in the eyes of government-that's wrong. But inequality in the eyes of society is quite natural. And to change it requires removing society's ability to express the differences in how they view those around them. Both economically and socially.