If the OP was never going to bring the RV into Idaho, it would be different. However, he stated that he will have the RV in Idaho for at least 51% of the time (suggesting that the rest of the time, he would be traveling in it).
In addition, New Mexico's MVD states that 2 forms of "proof of NM residency" are required in order to register a vehicle in New Mexico. California DMV does not indicate any such requirement. The obvious reason for that is because New Mexico does not allow non-residents to register their vehicles (military personnel being an identified exception), while California will happily take your fees regardless of where you're from.