so, if you look at Canada BEFORE the British conquest in 1760, the race mixture was a tad more prominent. Métis traders and trappers were far more common. Though to be fair this was not the case in the two main cities, only out in the wilderness. But it was not necessarily looked down upon either.

In Spanish territory it was, as you point out, far more common to the point where we have a whole ethnic subgroup called "Hispanic" (which of course if part of the larger racial group of "Latino". The reason we use that term (Latino, Latin America, etc) could shed some light on why this mixture was prominent there: CATHOLICISM. Seriously. Once the Indians of these regions were converted, they were no longer seen as "savages", even if they did not adopt European styles and habits (same for the French, but there was still some emphasis on "europeanization" in Canada). This meant that intermarriage was not seen as a serious issue as long as both parties were baptized Catholics. Religion was the great equalizer (in general, specific situations might not always hold to the ideal). Catholicism saw itself as t he "universal" faith and it didn't depend on one single culture to thrive.

In the English colonies where Protestantism was the norm, and specifically English Puritan Protestantism, there was an emphasis on doing everything "the right way" and that meant to be a good Christian one must also be a good Englishman. Instead of missions like the Spanish, the New Englanders and Some others set up what they called "praying towns" where Indian children could be taught English customs and culture as well as the gospel. It's amazing they had this theology that a "savage" couldn't be Christian until he was "Anglicized", when just north of them in Canada the Jesuits had a decent success converting the Huron and Canadian Mohawk just as they were in their own villages. The Jesuits even used Indian culture to fortify their preaching, rather than seeing it as a threat to it.

Again this is generalized, and I'm sure there are other reasons beside the religious difference, but the difference in theology of "mission" between old Catholicism and new Protestantism cannot be discounted

For Brazil, race mixing begun almost from day one, for a very simple reason. The native peoples that lived along the coast practiced polygamy, and it played a major role in power politics. If a tribe conquered another, the chief would likely marry someone connected to the conquered tribe’s chief. So, when the Portuguese arrived and didn’t find any obvious source of wealth, while the Spanish had found plenty of gold immediately after having contact with the native civilizations, they started a form of “private” colonization, where someone could rent a huge amount of land from the crown and do whatever they wanted there.

Soon it became obvious that being purely antagonistic to the native’s culture was gonna make colonization much more costly, so some of these early colonizers started playing along the power structures that were already in place, i.e. marry into the nobility of any new tribe they conquered. Despite the Church’s condemnation of the polygamy going on there, the Portuguese crown saw the results that tactic brought and even agreed to recognize the legitimacy of the children born from those many marriages. The most notable historical figure to practice this was João Ramalho.

When African slavery became the new engine of the economy in the late XVI century, the idea of freeing a slave to marry her/him was already socially normalized by the previous experience with the indigenous slaves.

Sources: Capital of Loneliness by Roberto Pompeu de Toledo

History of Wealth in Brazil by Jorge Caldeira