Here is the link for dps website discussing the information. That was some audit they conducted!
These were the factors:
New Mexico statute 29-19-12E requires that in order for a state to be recognized by NM, their provisions have to be “at least as stringent or substantially similar” to New Mexico. NMDPS has generally found six things that make a state substantially different from New Mexico, and therefore would disqualify that state from being recognized:
1. Permits issued locally rather than by the state;
2. No fingerprint-based background check;
3. Permits issued to persons under 21 years of age;
4. Permits issued to resident aliens;
5. No classroom (static) training required;
6. No live-fire (dynamic) training required.
Missouri: Mutual recognition between NM and MO.
Nebraska: Written acknowledgement in place
North Carolina: Written acknowledgement in place.
North Dakota: Recognizes NM permits. Received written acknowledgement.
Oklahoma: Written acknowledgement in place.
*New Mexicans traveling to the following states should know these states require written reciprocity agreements before NM permits are recognized: Mississippi, South Carolina, and Wisconsin. Invitations have been sent and New Mexico is waiting on responses.