Perhaps, though if any party can have a primary, it's not limited to just Democrats and Republicans.
And I don't think I ever said anything about "Democrats and Republicans"---as long as ANY party participates in a process that uses tax dollars to fund the process, then the election should be open. If, for instance, an election has Democrats, Republicans, Libertarians, Greens and whoever else, then THOSE PARTIES SHOULD PAY FOR THE ELECTORAL PROCESS in proportion to the votes they get (or their party membership numbers---whichever the legislature decides is the fairest method).
If the courts say the "open primary" is unconstitutional on "right to free association" grounds, they should also find that tax-payer funded primaries are unconstitutional on "taxation without representation" grounds. Let the parties go back to caucuses and conventions, paid for by their own money.