Springfield is right.
Many a locked gate, in NM and across the southwest, is a PITA. They aren't actually legal, but, they do get away with it. We have it here in South
Dakota, and in Wyoming, and there are tons of locked gates in Arizona, too.
A visit to the rancher is a good idea - however, if that doesn't work, there are legal ways to gain access. (assuming it is BLM land).
Note to the wise - leave a gate exactly how you find them - that is one of the reason for locked gates - folks leaving gates open and cattle wandering away, only to "pair up" with other herds, or worse, getting hit on roads or killed, and I can tell you from personal experiences - it is a PAIN, rounding up your cattle out of another's herd. Not to mention the fact that the BLM controls the leases extremely tightly. If there is one
cow/calf pair on land that isn't suppose to be there, you can get fined and lose all your leases. So, ranchers are picky about those kinds of things.
As far as state land - we had one deal, and one deal only, with New Mexico state land. How surprised I was that, after prospecting, assaying, marking off, paying for a claim, that the state of New Mexico then takes your claim and sells it to the highest bidder in a public auction. (HMMPF),
For uranium claims, I can see that - but......................they do it for all.
Beth