You need to remember that just about every single country in Latin America has had its government either overturned or infiltrated by the United States in the past 50-70 years. The governments instilled in those countries are more like the Republican party, and thus, Republicans seem like a more comfortable choice for Latin Americans than something like Democrats- whose puppet equivalent in those countries are useless seat fillers meant to showcase "how good the conservatives are in comparison". Latin American politics is just a more extreme version of USA politics but with the without what little façade the USA pretends to have.

It's not really weird.

Also, just about every US president, Republican or Democrat has put immigrants (legal or otherwise) into cages and split families, or conveniently let them be slave to farms and hotels. To immigrants, there's no difference between the parties.