Last week, while in a group chat during a teacher conference, Idaho Secretary of State Ben Ysursa (a Republican) was asked if he would show up at the court oral argument a few days hence, in the case of Idaho Republican Party v. Ysursa. Ysursa smiled and said he might not attend all of it, because he was also planning to be travelling around the Treasure Valley on the GOP unity bus.
The joke reflects neatly on the catch the Idaho Republican Party is in. It may be the the most electorally successful Republican Party in the 50 states - the trial brief for Ysursa and the state of Idaho argues specifically that it is, and the point would be hard to dispute. But the party structure and leadership has gone so far as to sue the state (which is overwhelmingly governed by Republican officials) to change the way primary elections are conducted, on the argument that the party is being damaged by the way Idaho runs them.
The Idaho system (which is different from Oregon's, which is also different from Washington's) allows voters at primary election time to choose a ballot from one party and stick to the contests within it (along with some non-partisan choices, as for judges). But voters do that in secret; there's no way of specifically knowing which party a staunch Republican or Democrat chooses while in the voting booth.
And it would be hard to sell the idea that within the Republican Party, conservatives are being shut out by primary elector voters. This year's Idaho primary, for example, was most notable for the defeat of relatively moderate candidates by more-conservative ones in a string of races - hardly an indicator of Democrats or Democratic sympathizers exerting a lot of undue influence.
Still, in their brief, the party argues that a lot of voting in Republican Party primaries by non-party members occurs. And there's no real doubt that it does. It cites a Moore poll saying that 39% of non-Republicans who vote typically vote in Republican primaries. The state brief attacks the methodology, but intuitively, the Moore number seems somewhere about right. (Polling indicates that somewhere around a third of Idaho voters consider themselves independent, but very likely few refrain from voting in the Republican primary.)
The party also tries to nail down a degree to which this affects the end results, and that is almost impossible to know for certain. Crossover voting seems to be extremely hard to orchestrate, and serious efforts at orchestration don't seen to be very common. None of which may matter. Even the fact that it may be unknowable in a conclusive way sort of helps the party's case.
The case may turn on the question of affiliation: To what extent do members of a political party get to choose who they affiliate with? The state (defending the current system) said the right is de minimis - minor - while the party suggests it is much more central. It may be hard to control even in places that require overt party registration. In Oregon, for example, where voters register by party preference (or none), voters can vote only on the primary for which they have publicly expressed a preference. But that doesn't stop some voters from switching to another party just before a primary, and back just after. Still, party registration could be a party-strengthening tool. (What you think of that may depend on what you think of the parties.)
The party and state briefs are not very long and well worth the read. Mark this down as a case that could realistically go either way.