In Trump v. Anderson, the Supreme Court is taking up the questions of whether Donald Trump can appear on the Republican Party primary ballot. This ballot is administered by the State of Colorado, and Colorado law requires that any candidate appearing on a primary ballot be "eligible" to hold office.
However, the Republican Party is a private organization, not a government organization. I would have thought that under the recognized right to freedom of association, the GOP should have the freedom to select any candidate they want to lead their party, even if that candidate can't possibly hold office.
That said, I haven't heard this argument come up in the news coverage of Trump v. Anderson, so either I'm misinterpreting something or this is already settled law. Why does a state have the right to say anything about the candidates in what's supposedly an internal election for a political party? Is there any case law discussing these or similar restrictions on primary candidates?
(I readily accept that the state has an interest in ensuring that candidates appearing on a general election ballot are eligible to serve. My question is strictly about whether the state has a legitimate interest in requiring that political parties nominate "eligible" candidates in a primary process.)