I do see Mexicans who are afraid to come to the U.S. as illegals being willing to use a legal means of getting their families out of abject poverty. Not all Mexicans are after the free meal, free money aspect. I know a lot of legal Mexicans that bust their butts doing jobs I wouldn't do.
Then, yes, I would be okay with granting asylum to homeschoolers from there and everywhere else on the planet, provided that they are not otherwise enemies of the principles on which this nation was founded. I would be okay with granting asylum to all of the Christians being persecuted around the world as well. We could use more of them.