I know of no progressive that supports unlimited immigration with no screenings, that is a right wing talking point based on nothing factual.

I do see a lot of people on the right, some conservatives, and some libertarians calling for blanket bans on entire groups of people based on dubious claims and hypotheticals.

It's a hard argument to make that banning an entire country from opportunities/immigration is "treating everyone as an individual".

“No person is illegal” is a very popular progressive slogan and lawn sign and if that doesn’t mean unlimited immigration it doesn’t mean anything.