Mexico has been a democracy for some time now --- and I've been there quite often and I've seen what they did with the vote in their own homeland. Why would crossing the Rio Grande or the desert turn them into instant Republicans? It certainly didn't give them instant job skills, education, or health insurance.
They are like all of us, Capitalist by nature, but capitalism has issues that get sorted out in later generations with education.
When my parents came here, they worked their butts off to make sure I got and education. Because of that I employ 22 people, I grew to be a Reagan Rep.
You mention instant, nothing is instant. If that were the case we could protect our borders overnight and that would solve the problem.