Further, many groups of immigrants regardless of origin initially vote Democrat(though it does vary by background). Some for the same reason simple-minded white leftists do(Hollywood), on the face of it Democrat ideals SOUND good and appealing. For some it takes awhile to actually see through the lies, to experience the reality. And being poor, often it is simply out of self-interest. If you are struggling and someone offers you a handout, the temptation is to take it and not ask too many questions. I think many here forget that for some there is a political learning curve. That doesn't mean excuse it, but rather factor it in when explaining conservatism and deciding whether or not to reach out to 'other groups'.
Now all that I agree with. We've had a huge influx of immigrants in the recent decade, sometimes that learning curve is over a couple generations. You've also got an unemployment rate over 20% in some of the border counties and those counties are growing in number. You've got millions of people who are easy prey for the Sanchez type politicians because they don't speak English even though their grandchildren may eventually speak English and won't be pandered to as well. But in the meantime we could lose Texas to the Democrats and then the problems begin.
What you've said here sums up much of the danger to the Republican Party posed by mass immigration both legal and illegal.
The illegals are mostly "economic refugees" fleeing poverty and running to America's jobs and social programs. Most of the legal immigrants come here broke and start working their way up from the bottom. They are overwhelmingly future DemocRAT voters.
What does a recent immigrant care about American conservatism. They want to establish themselves in America and will accept any hand that will give them a hand up or a hand out. (And I speak from a great deal of personal experience with recent immigrants having been born in NYC and now living and working there). Later as they become educated and accumulate earning power and assets they may want less government , less taxation, and less social programs. But this process takes time. The problem with current mass immigration is that too many people are coming in too fast. The numbers are so great that they are exerting too much influence in American Politics. America is not assimilating them, they are changing America. America is not giving them the time to become educated and learn about, for example American conservatism.
They are adding large numbers of voters to the Democrat registration rolls.