I grew up in Manhattan, from the wonderful late sixties right through the worst of the 70s-80s. But I tell you, rich and poor lived in the same neighborhood. I went to school with some extremely wealthy people and some extremely poor people. Poor white people too, fwiw.
I never realized we had a class system in America until I saw the movie “Caddyshack”. It was a complete revelation to me.
Some things have gotten much, much better in this country over the ensuing decades, but our system of class striation has gotten much, much worse.
I went to Prep School in a wealthy neighborhood, Shaker Heights, Oh. I lived in the dorm, and the locals made sure we dorm rats knew about class distinctions.