I think that change has to pass through the legislature of each state concerned. I may be wrong, but I believe the party muckity mucks make the rules for the primaries. As a delegate for my district and state conventions I could not find out exactly WHO made the rules for the primary.
I sat with my state representative and my local party chairs, outgoing and incoming, at the state convention and never got a straight answer.
Perhaps you can get an answer to the rules for primaries question by going to a law library (or a good public library) and looking at the state statutes of the state under consideration. I would go to the comprehensive index of the state statutes and look up "Elections" and/or "Primary Elections." Then look up the section(s) listed and see if there is a reference to voter registration for the primary by party. I would guess there would be, and the statute would spececifically state if the primaries are open to all voters (open) or limited to party registrants (closed).
BTW, there are states with no formal party registration, so it would be impossible to run closed primaries there until party registration of voters is introduced.