As someone not born in America, I find the politics surrounding it quite odd as well.
I've lived in 5 different countries so far (ranging from developed to developing), including the US, and what makes the US stand out is the lack of immigration enforcement. It's wild that you can enter the US illegally (or overstay) and, until recently, live your entire life without much concern. You can be employed illegally, go to school, get a bank account, pay taxes, and even be charged with a crime, serve a sentence and be released, without anyone bothering to see if you're in the country legally.
Every other country I've lived in takes immigration seriously. If caught in the country illegally, you're deported very quickly and pretty much banned for life from coming to the country again. Police and the courts enforce immigration laws, employers face serious penalties for hiring people in the country illegally.
And practically nobody in those countries bats an eye. They see it as normal as enforcing any other law.