On May 7, Arizona filed this brief in the U.S. Supreme Court in Arizona Libertarian Party v Hobbs, 19-757. This is the case over how registered members of a small ballot-qualified party that has been on the ballot for at least four years can get themselves on the ballot.
Ever since the new law was passed in 2015, no Libertarian has been able to get on the primary ballot for any congressional race, or any state race.
The Arizona brief does not mention the point that Arizona has extremely easy primary ballot access procedures for small qualified parties that have not been on the ballot for four years. This is why many Green Party candidates were able to qualify in 2016 and 2018, when the Green Party was on the ballot.
The Arizona brief claims there is no circuit split, but there is. The Third Circuit struck down a somewhat similar Pennsylvania law in 1985 in Consumer Party v Davis. The state claims the Libertarian Party doesn’t have any support in Arizona, but last time it was permitted to have a candidate for Governor, in 2014, it polled 3.81% for its nominee Barry Hess.