Isn't pulling business out of Georgia the same symbolism as sanctions against countries? Only the people pay the price, never the leaders?

The difference is that Georgia is a democracy.  Sanctions as a political tool are often ineffective against dictatorships like North Korea or Russia.  That's because they're not democracies and the elites can insulate themselves from the practical impact of sanctions, forcing the hardships onto their people.  But they can be effective as a political tool against democracies.  That was the case with South Africa which was, for its white residents at least, a democracy.   Apartheid eventually fell in part because white South Africans got tired of living under sanctions and preferred political reform which dismantled Apartheid. 

Georgia is a democracy.  The people still control the government (although Republicans would like to end that).  So sanctions could be effective at pressuring the government to change because the people who will suffer have ways of taking out their displeasure on the leadership.  This has worked before.  A few years ago, economic pressure worked to force North Carolina to soften an anti-transgender bill which they had passed.

I don't know who is more intolerant-

Georgia or those who are boycotting the state.

One other point- there are about twice as many whites those restrictions affect as there are blacks. When the news and others call it racism they ignore over half of those living in poverty in that state.

I think the idea is that the people affected will put pressure on those leaders. Kind of like how the Civil War didn't really get serious until the people of the south put pressure on their leaders to give it up already before people starved to death. 

Georgia brought it on themselves, what is happening.

And yet they call for unity. Well, they lie about unity a lot too. They aren't to be taken seriously.