Right, would be no problem there.
But here, I wouldn’t want to not be able to vote in the GOP primary.
I’m reminded of the now-illegal “blanket primary” setup they had in Cali.
California changed it to something very similar to the LA jungle primary, the only difference being that the CA jungle primary takes place on primary day, with the top two finishers going on to Election Day even if one got a majority, while in LA the junge primary is on Election Day and, if no one gets a majority, the top two go to a runoff in early December. The courts have upheld jungle-primary systems, but I would strike them down as violative of the First Amendment rights of citizens who form political parties to petition the government for redress of their grievances and who are denied by such law of the ability to select their party’s standardbearer for the election.