Think you'd have to look it up state by state. CA for example, has top-two for state-run elections (like the governor) but closed primaries for the US presidency.

And then you have caucus states, which aren't primaries which is better.

The CA Republican party (joined by Peace & Freedom and Green parties iirc) actually sued the state and won, because the state wanted open primaries. The winning counter argument was freedom of association under the 1st amendment.

Think you'd have to look it up state by state. CA for example, has top-two for state-run elections (like the governor) but closed primaries for the US presidency.

And then you have caucus states, which aren't primaries which is better.