Their electors should be rejected.
That setup in N.M. is insansane. I can’t imagine how anyone could imafgine such a system being used. The votes from that state (for federal elections at least) should just be considered invalid & then I would think that the citizens would demand that actions would be taken.
You can’t demonstrate effort to avoid voter fraud, and illegals and people from other states voting twice, then your elections don’t count for national offices. You don’t get your electors seated, and they don’t count for Federal elections nor do they get seated for the House. Senate must be by state legislature appointment in these states. No voter integrity means limited voice in FedGov., and absolutely no Federal money or subsidies.
That’s what needs to happen.