I don't know - i'm a relative newcomer here in New Mexico, from the SFBay area.... but aside from Big Oil money (from the oilfields in the southeast part of NM - and the border with Texas and more oil families who also are very close with Gov Susana Martinez (R) and her gubernatorial campaign funding - the rest of the state seems more embued with interests and a sociology more relaxed; it's mixed ethnically, involved with "spiritual" things (at least in Santa Fe and Taos areas....), has a huge hispanic and native american segment of the total population, which is pretty sparse compared to most other states, I think (I haven't looked that up, so don't shoot me just yet). Much of the industry here is tourism, service industries, and state/local government (Does that lean more toward Democrat? perhaps). Farming and ranching are very traditional here where the Rio Grande flows through New Mexico; large plots of land but not necessarily a large income from them; many small family plots to grow just for the household = workers. "La familia", the Catholic Church and the community are big concepts historically and currently which may affect the politics, too., to bend toward democratic ideals vs. Republican. Those are some of the influences I think make New Mexico more blue except for the southeast counties (near TX).
Arizona? Not sure about why it's so Republican - other than the dominant white culture in two main urban areas where the money is. You'd have to ask the AZ members here on RJ for their opinions there. New Mexico has much more Spanish Colonial residual culture than AZ - perhaps it's the history of the region, including California. Of course all 3 states/areas share a common Spanish/Mexican colonization and rule going back 400 years or more in some areas, not all of it pretty. But the modern history is very different among the 3 states.
Whatever the reason for being largely Democratic, there are lots of Republican bumper stickers too - those perhaps with lots of money from out of state who own second or 3rd homes here? - There is definitely a large group of very wealthy people in Santa Fe - the real estate prices, costs of living, etc. are higher here than elsewhere in the state. Santa Fe also has the third largest art market in the USA, after NYC and Los Angeles, I've read. The sticker prices are VERY high. Somebody is buying the art, and the city has lots of rich donors to foundations, the opera, the museums, other cultural and civic endeavors. Thank goodness! Yet we still have a reputation of being "Democrats"