Think New Mexico, a non-partisan think tank, has asked the Republican Party of New Mexico, and also the Democratic Party of New Mexico, to amend their bylaws and let independent voters participate in their primaries. See this story. New Mexico was one of the last states in the nation to even have primaries. Until 1938, all parties nominated by convention. Primaries have existed since 1938, but have always been closed.

Here is more information about Think New Mexico. The group understands case law, and in its advocacy to the parties, correctly points out that the decision on whether to let independents vote in party primaries is a decision for the party to make, not a decision for the state.