I'm majority Cherokee yet I didn't grow up in the culture. Didn't even know until I was in my late teens. I was raised with my mother being Cherokee/Dutch/German, my stepdad being Italian born in New York. Which basically meant I was raised in a big loud annoying Italian family (grandparents lived down the street) that said "fuck" a lot and went to a Roman Catholic church on Sundays to be forgiven for saying "fuck" a lot.
My biological father lives in Oklahoma on the Cherokee nation reservation (I think it's called a sovereign nation now?). Met him once as an adult. I share the Cherokee bone structure (and blood), but the rest of my features lean towards the Dutch/German/Irish side even though i'm majority native. Basically, I'm white as fuck with blue eyes and reddish blonde hair, yet I can shoot a bow and arrow like a sniper.
I can honestly say even though my heritage is majority native, I have yet to meet a full blooded Indian. I never had the opportunity to gain acceptance into the Cherokee tribe due to looking "too white", yet I'm still able to apply for residency on the Cherokee nation in Oklahoma.
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I'm embarrassed to say I've never looked at it that way, but you're absolutely right.