New Mexico was also once part of the Spanish Empire, for more than 200 years for that matter. But no one would mind if they ran the Spanish flag up the pole, because Spain poses no threat to the integrity of American rule.
Actually, I would mind it, if they ran the Spanish flag up the pole, if it were done at a governmental site, and it was being flown in a place where the Stars and Stripes generally flies.
Now, if the Spanish flag, or a Mexican flag, were being flown at a consulate, or at a private residence (of *legal* residents), that would be fine.