I'm pretty sure this is legal, but I love my freedom and want expert advice. Can I travel with an AR- pistol from Colorado through New Mexico to Arizona? in a rental car? through tribal land? or just bring a 1911? or nothing? I follow the law.

Yes, AR-pistols are fully legal in NM. There are no mag limits/restrictions, etc. As long as your AR-pistol is legally setup by Federal standards you should be golden.

Car is an extension of your home in NM and open-carry is legal. No issues there.

Not LE hopefully BURN will chime in but I have carried and traveled in the three states in question and have never had an issue.
I did have LE on a reservation in NW NM freak out like 12 year old girls from NYC encountering there first snake and spend 30 minutes checking me out and unloading all my weapons and placing them in my trunk for safety.
Pulled over on 40 for a bad headlight on a rental...
It was a win as I stopped at the next Walmart to see if I could get a bulb and scored 1000rds of WWB 9mm for $200.

Thanks for the info everyone!  I just wanted to make sure