The Tenth Circuit has decided Beaver v. Clingman. The case involved the constitutionality of Oklahoma’s semi-closed primary objected to by one Oklahoma’s political parties. The case presented a pretty clear-cut application of two earlier Supreme Court cases holding that states may not impose a particular form of a party primary against a party’s consent.
As the court explained:

This case falls between Tashjian and [California Democratic Party v.] Jones. Whereas Tashjian concluded that states could not restrict parties from allowing independent voters to vote in their primaries, and Jones held that states could not compel parties to allow voters from other parties to vote in their primaries, the instant case asks whether it is permissible for states to forbid parties from allowing registered voters from other parties to participate in their primaries….
When read together, the clear and unavoidable implication of Tashjian and Jones is that a state generally may not restrict the ability of a political party to define the group of citizens that will choose its standard-bearer. That conclusion dictates the terms of our present analysis, for among Tashjian, Jones, and the instant case runs a connecting thread. In each of the three cases, the regulation at issue restricted the options of parties seeking to define the scope of their associational rights. Faced with the prospect of such burdens in Tashjian and Jones, the Supreme Court employed strict scrutiny. Given the similarities among the cases, we are compelled to exercise similar vigilance here. Because we conclude that the burden in the instant case is a severe one, we proceed to analyze whether the regulations are narrowly tailored to serve a compelling state interest.

The court then rejected the interests put forward by Oklahoma to justify its law. Of course, this ruling only applies to party primaries. To the extent a state does not hold a party primary to choose the parties’ standard-bearers (as in Louisiana), Jones makes clear that the parties cannot object to the form of the primary. (Disclosure: I am a consultant for the proponents of such a primary in California.)