Earlier this year the Catoosa County (Georgia) Republican Party refused to place some candidates for county office on its May primary ballot, because the county party officers felt the candidates aren’t “bona fide” Republicans. Georgia does not have registration by party so there is no objective method to determine who is or isn’t a party member.
A trial state court then put the candidates on the primary ballot, and they won their primaries. The county party appealed to the State Court of Appeals, but the State Court of Appeals transferred the case to the State Supreme Court. The State Supreme Court said the party was negligent in taking too much time to appeal, so dismissed the case on those grounds. Thus the bigger issue of whether parties in Georgia can block candidates from their primaries on political grounds is still unresolved. Precedent in Georgia says parties can block presidential candidates from their own presidential primaries on political grounds, but it is still not clear whether that principle applies to other office.
Here is the decision in Catoosa County Republican Part v Henry, S24A0917.