I’m honestly surprised the open carrier wasn’t harassed by the cops. In New Mexico, you cannot legally open carry into establishments that sell alcohol, any alcohol. Most, if not all, gas stations sell alcohol (in NM, distilled spirits, wine, beer, mixes, etc... can all be sold in these places).
INCORRECT: Handgun Law: NM
Read the bottom half of page 4 and the top half of page 5 where the law is cited. All things considered, it's easier to figure out the carry rules as regards restaurants serving alcohol than it is to be certain you're not afoul of the rules of an Indian tribe because you crossed some line on the map without noticing it.