New Mexico primaries are closed. That results in about 1/4 of the eligible voters NOT being allowed to vote. Independents are not allowed to vote because there is no "Independent" party. I would suggest the primaries be closed but Independents can vote for either party's candidates. There would be a ballot for Republicans, a ballot for Democrats, and a ballot listing both parties for Independents.
Then everyone would register as Independents to keep their options open and then you have an open primary again.
I think letting each party decide which registered voters they will accept would be better. Like the Republicans accepting both Republican and Independents but not Democrats.
In Massachusetts, Independents can vote in either primary, but we have to choose either a D or an R ballot -- no mixing and matching! And if you want to change your party affiliation, it has to be done about a month or 6 weeks (I think) before the election. Doesn't seem to be the case in Mississippi.