More like the 20th century when most of us came here, NOT the 1800s, and those prejudices and bad behaviors are STILL HERE. Both sides of my family came here between 1910 and 1950 and the issues continue today. I grew up with them in Virginia and Washington DC (70s-90s), and still experience them in SoCal now. Whites still view me as a different race, whether they should see a difference or not.
People who care about being White consider me a mongrel, and White Supremicists have me on their kill list, full stop.
You see me as only White and having the advantages thereof, sometimes yes, sometimes no, usually with dangerous results. Neither you, nor the experts in modern race theory are totally on about everything OR this, or I would be able to go 3 months on a dating site without being called horrible things or immediately discovering that a date didn't think treating me with respect was necessary if they were White. Whoever came up with this idea had NO CONVERSATIONS with minorities like mine. NONE. They they just ran with their theory.
A bunch of people including Italians, Jews, Slavs, and Romani did not "become White" or enfranchised. We probably did become somewhat powerful, insular minorities, but we’re still minorities. Modern race theory would have you believe that for their own purposes, but the discimination, exclusion, violence and dismissiveness remain. We're only conditionally White. We statistically join numbers when they need us, some are respected professionally, but that's about it. You have "education" but not experience.