There's an easy solution to "illegal" immigrants: Have a recognised and published legal program for seasonal itinerant workers such as crop-pickers that gives them a legal avenue to be in the USA, perhaps for a limited time, in specific locations, for specific purposes (or any combo). I suspect this already exists, so any USAian can inform us.
The problem is that "illegal immigration" isn't really the issue that ICE is trying to address. That's a furphy, an excuse, a front for what they are REALLY wanting to do. It is, as you say, making the USA into an all-white, heterosexual-only, paternalistic, fascist regime. Gilead. And that means all the "non-whites (definition to be supplied by ICE)" have to be removed.
If this keeps up, I will not be surprised to see women, especially outspoken women who oppose this regime, become targets as well. They are already picking the ones in hijabs. How soon before the ones in wimples, scarves and hats are next.