The nation’s first winning challenge to open primaries (as opposed to blanket primaries and top-two primaries) is now over. The case Miller v Brown, from Virginia, has ended. This is the case in which the Republican Party of Virginia sued in 2005, alleging that it has a constitutional right to exclude non-members from its primaries. Both the US District Court, and the 4th Circuit, gave partial relief. The period for either side to appeal to the U.S. Supreme Court has ended, and neither side sought U.S. Supreme Court intervention.
So, the decision stands. The Republican Party bylaw can be implemented in cases in which the party is being forced to hold a primary. But it may not be implemented in situations in which the party is free to decide whether to use a primary or a convention or caucus. The Bylaw says any subunit of the party may require that people who voted in the Democratic primary in the last five years cannot vote in a Republican primary unless they sign a pledge that they are loyal Republicans.
The only other lawsuit pending against open primaries is the Mississippi Democratic case, which is pending in the 5th circuit.