Open Primaries and the "Top Two"
Below is one of my comments from another website. It's a response to Jim Riley of Texas.
My state has state-mandated open primaries, in which each voter picks a party on primary day. The only change I personally favor here is the elimination of party primaries for county and municipal offices. Nevertheless, the federal courts for some 35 years have been ruling for greater autonomy for political parties. Just look at the reasoning, e. g., in the California Democratic Party v. Jones blanket primary case, and it’s not hard to predict what the U. S. Supreme Court will say about the state-mandated open primary.
Let’s say the Supreme Court hears the Idaho case and strikes down its state-imposed open primary (Idaho Republican Party v. Ysursa). The Idaho Democrats have indicated that they will keep their primaries open to ALL voters. And any party in any other open primary state that did not want an open primary for itself would have to file suit. It would be an easy case, but it would take time.
The Mississippi Democrats brought suit against the open primary in 2006 (Mississippi Democratic Party v. Barbour). They said if they won, they would invite independents but block Republicans from Democratic primaries. The Mississippi Republicans, for their part, indicated that they would keep their primaries open to ALL voters (that case was dismissed on a legal technicality).
So even if the high court strikes down the state-imposed open primary, there will continue to be open primaries. The difference will be that the parties– not the state– will decide who is eligible to vote in party primaries (the state does have the power to prohibit parties from inviting members of opposing parties to vote in their primaries). Even if a state can no longer force open primaries on parties, the parties will still be concerned with staying in the voters' good graces.
I think you’re engaging in wishful thinking in your prediction of a massive proliferation of the Louisiana-style “top two” system. State legislatures are very unlikely to mandate the “top two” for state or congressional offices, and many states don’t have the initiative process.
No states now leave it to parties to maintain their own records for the purpose of excluding some voters from their primaries. In every state where at least one party wants to exclude some voters, the state registers voters by party (29 states and the District of Columbia now have party registration).
 In a blanket primary, all the candidates of multiple parties are listed on the same ballot. The top vote-getter from each party moves on to the general election, where any independent candidates are also on the ballot.
 All candidates, including independents, are listed on a single ballot. The top two vote-getters, regardless of party, advance to the runoff.