How were some ways that different Latin American nations liberalized in terms of race relations? The American South gets a lot of criticisms and focus for the barbarities there, but surely just as much tension and injustice exists in Latin America. So how did those countries solve their racial issues? Could any of such methods apply to the South?
The race question is very different in Latin America. Race-ideology was developed in the U.S. to rationalize the contradiction between the proclaimed principles of American democracy and the practice of slavery. This led to such practices as the formal bans on interracial marriage and explicit race-limits on citizenship.
Latin Americans had fewer scruples about slavery, and never developed the ideology. Also, there was far more intermarriage between Spanish colonists and the Indian natives, and also with black slaves and ex-slaves.
So there was never a strict "color bar" as there was in the U.S. by 1800. While there is a correlation between race and social class, people who would be considered not "white" in the U.S. could rise to the highest levels of society.
For instance, Cuban dictator Fulgencio Batista was a mulatto: that is, part black. He rose to power by leading the "Revolt of the Sergeants" in the 1933 Cuban revolution. The new regime elevated him to commander of the army. He used control of the army to dominate the government and in 1940 he was elected President. None of this would have been possible for a black in the U.S.
It should be noted that Latin America has far worse class issues than the U.S. and these correlate substantially with race. For instance, the success of Chavez in Venezuela was in large part due to his being visibly mestizo, and appealing to the resentment of the mestizo masses against the nearly all-white elite who were seen as running (and looting) the country to suit themselves.