Does New Mexico feel like Mexico or not really?

I live in New Mexico (Taos) and I'm curious how much New Mexico feels like Mexico. There's this whole ordeal where people here say they are Spanish and not Mexican - but how different is it really? Is the Spanish here interesting sounding? Does it feel like archaic Mexico that landed in the US? Or does it just feel gringo?

There's hippies and communes in Mexico too right? There's a lot of indigenous heritage pride here, but that's true in Mexico as well right?