Here are a few sources I found but they don't segment income level.
2018: https://www.pewresearch.org/politics/2018/03/20/1-trends-in-...
2015: https://www.pewresearch.org/politics/2015/04/07/a-deep-dive-...
https://dasil.sites.grinnell.edu/2020/05/the-demographic-pro...
Latino Americans are still overwhelmingly left-of-center (though perhaps not likely to be left enough to be "leftist").
The shift to the right has been relatively small (though consequential due to geography) and limited to certain groups. For example, Cuban Americans in Miami are much more likely to have moved to the right.
US conservatives are protesting and restricting immigration when in New Zealand, the conservatives are wildly pro immigration. Their argument is that it drives house prices up and wages down when you've got more people flooding in. If you're a land and/or business owner, that's what you vote for. The left wants less immigration so workers and renters have more negotiating power.
Once the population becomes more diverse from immigration, they will perhaps become nativists because their base will drift that way.
There may be conservatives who oppose immigration out of xenophobia, but there are many conservative business owners who see immigration as a way to keep paying a less than living wage, and landlords who see it as a way to keep the demand for rentals (much) higher than the supply
[1] https://store.cato.org/collections/frontpage/products/the-mo...
[2] https://www.cato.org/white-paper/fiscal-impact-immigration-u...