I am not the one throwing around the word "native" casually. To cite your example, Salt Lake City was founded less than 200 years ago whereas Puebloans have been living in the area for several thousands of years.
You can certainly make a claim that Mormon culture is "native" to Utah, but I think at 200 v/s 5000+ you can expect that claim to be contested.
Funny enough, the definition has nothing to do with ancestry. "Native: a person born in a specified place or associated with a place by birth, whether subsequently resident there or not."
Yeah, this is the exact sense in which I wrote it originally - but I sensed the screams of 1000 idiots and wrote "native" to try avoid that entire line of conversation. It seems though that my efforts went unnoticed - oh well!
You can certainly make a claim that Mormon culture is "native" to Utah, but I think at 200 v/s 5000+ you can expect that claim to be contested.