On November 8 and 9, two interesting amicus briefs were filed in the U.S. Supreme Court in Utah Republican Party v Cox, 18-450. Here is the amicus of CATO Institute, the Pacific Legal Foundation, and Freedom Partners Chamber of Commerce.
Here is the brief of Private Citizen.
So far the state of Utah has not waived its right to file a response. The issue is whether the First Amendment’s Freedom of Association clause protects the right of a political party to decide for itself how it nominates candidates. The Utah Republican Party is willing to nominate by primary, but it wants to limit individuals on its primary ballot to those who have shown substantial support at a party meeting.