That was only really was true from 1968-1988 and in 4/5 elections republicans won by such large margins that if the had won by those margins today NM would still vote Republican.
In 1976 Carter was a terrible fit for that state , and 1968 in not sure why it voted GOP .
Lastly is that 1968-1988, the new deal coalition was quickly falling apart(or by the 1980s had fallen apart) while the GOP suburban + rural coalition was getting stronger and stronger , thus the GOP was able to sweep the sunbelt while the Dems were searching for a new coalition.
Decent answer, but still neglects some fundamentals when it comes the both the decreasing vote share of Ancestral Democratic Miners within the State, the fast net In-Migration of SoCal Anglos between '70 and '90, as well as the "Old Spanish" populations in the State that traditionally tend to vote more "Anglo" rather than relatively newer populations whose Country of Ancestry might well be more Mexico or places in Central America....
Simplest answer might be a mixture of the "Sagebrush Rebellion" combined with wealthier (Upper Middle Class) voters in the State backing 'Pub Pres GE candidates that were heavily SoCal retirees in order to both obtain tax breaks, as well as dodging having to actually pay for Public Schools indirectly because of their personal property tax issue.
