but you have due process that allows varying methods of allowing illegal immigrants to legalise their status.
Whilst they are following those due processes they are allowed to stay and if State law allows even hold official positions.
All done by the Great American Rule Book

Only once they have exhausted the relevant d process are they liable to deportation.
Similar sort of thing happens in a lot of countries
Side note:
The USA is more like the EU now that I think about it.
A ragtag collection of countries/states with their own legislations which may/may not be at odds with the higher level legislations.
Califormia (as I understand it) deliberately changed their laws to **** off Trump
Again, not ILLEGAL aliens. Illegal aliens should not be doing anything here except looking for the nearest exit.
You are talking about legal aliens of one type or another, and that is fine with me, and I think, most Americans. A 'green' card, a visa, permanent resident status, diplomatic posting, a work visa.... there are many ways to be in the US legally while NOT being a citizen and no one I know is opposed to that.
Brian