I don't think it's up to the GOP, although they have a lot of sway in the Legislature and the Ninth Floor..
The current "official" take is that only registered Libertarians may vote in the Libertarian primary, but Republican and Democrat primaries are open to registered members as well as independents, EXCEPT that presidential primaries are not legally "primaries" but internal party business and only registered party voters may vote.
The difference between the Libertarians and the R/D's is because the Libertarians filed suit over the issue and won, and the Republicans and Democrats weren't party to the suit. Strangely, you'd think if that suit hung on an interpretation of law, the result would apply to all the other parties anyway, but evidently not.