First, there is considerable evidence that ethnicity/religion dont really explain the "sectarian violence" you refer to. Jim fearon and David Laitin argue in "Ethnicity, insurgency, and civil war" that civil is best explained by factors that favor a successful insurgency: a weak state, mountainous terrain or jungles, so on and so forth (imo weak state is the important one). Collier and Hoeffler take a more economically focused study and argue that grievances such as political marginalization or ethnic oppression also fail to hold water in predicting intrastate conflict. Instead, the economic viability of revolution--availability of finance, lack of economic alternatives to would be rebels--is a stronger predictor.

In this sense, the sectarian violence you see is not just ethnic tension and isn't really explained by colonial legacies. While that tension is real, it does not explain why t countries see more violence than others. Weaker governance (Somalia is essential non existent), availability of conflict resources (diamonds in west africa are a classic example but we also see ISIL and oil), and support from foreign governments (think Hezbollah/Hamas) explain the violence you hear about in the Middle East and Africa.

Finally, latin and south America have seen some very serious violence from paramilitary groups. FARC in Colombia may be the best example. Ostensibly, they are a Marxist revolutionary group fighting against the capitalist/imperialist threat to Colombia's common people (ie the government and the United States). However, one cannot explain FARC's existence without also examining Colombia's weak government, failing economy (except for narcotics used to finance FARC), and support from the Soviet Union. Beginning in the 2000s however, Colombia's government became more consolidated, the viability of the drug trade decreased, its economy developed, and of course the soviet union collapsed. Is the capitalist/imperialist threat any different? Maybe but I dont think it explains the increased peace and stability in Colombia as well as the factors mentioned above.

I will talk about Brazil (and Portugal) because I'm from Portugal and know about those countries situation better than the others.

If you're talking about racial hate, then there's a obvious reason why it's so low in Brazil.

Brazil was inhabited by indigenous people from AMERICA, then in 1500 was colonized by Portugal (EUROPE) who also bring slaves from AFRICA.

For e.g., In the USA, England (EUROPE) killed most of the indigenous people (AMERICA) or at least isolated them in restrict areas, so most of the people living in there are direct descendants from Europeans and have no native (American) blood; And even you think about the Afro-Americans must of them are 100% black, so you either have Europeans or Africans, and no "Afro-European"

In other hand, in Brazil, they all mixed up between them, so it isn't rare to find a person in there that have European, American and African ancestry, that fact makes pretty stupid to hate someone from another race since you have a bit of them all. In some case you could probably even find a 4 in 1, since there is a big community of Japanese people living in Brazil.

And if you go to Portugal (which colonized Brazil) you can see that we're not 100% white, but a little mixed.

The portuguese ancestry is made by Celts ("very" white), Romans (white), Visigoths (white), Moors (black and "arab" skin colour), African people (black), etc...

So when Portugal colonized Brazil it wasn't strange to a Portuguese to mix with another race since they are also already used to it, the same goes for the African slaves who are also used to marry with portuguese colonizers. That din't the happen in USA since English people are pretty much 100% white and even despite they aren't racists they still thought it would be weird a white man to have kids with a black women or a white women have kids from a american native.