White people have the privilege to not be lumped together in our society

Calling them "white people" does lump them together. There's a fascinating history about how different ethnic groups got absorbed and assimilated into whiteness. You aren't supposed to look into your family's roots in Europe. That's woke nonsense! Just shut up, drink your beer, grill your steaks, watch football. You're white now.

BTW, I have heard people referred to as European-American. If your ancestors came from, say, Ireland, England, Spain, and Italy, you could call yourself an Irish-English-Spanish-Italian-American, but European-American is much easier to say.