The Penitentes, an ascetic Catholic group. https://en.wikipedia.org/wiki/Penitentes_(New_Mexico)
The Crypto-Jews, usually thought to be a hundreds-years-old vestige of Judaism fleeing the Inquisition. The truth is probably more complicated. https://www.theatlantic.com/magazine/archive/2000/12/mistake...
New Mexico is also home to a bunch of different Native American languages and cultures, many of which did not have the trauma of being forced to move to new land and thus have a different relationship with their history.
(This post feels clumsy of me, apologies if as an outsider I mis-characterized something.)