I'm not American, so I could be wrong on this, but would they have the ability to do so? My impression was always that the party doesn't necessarily have the po

I'm not American, so I could be wrong on this, but would they have the ability to do so? My impression was always that the party doesn't necessarily have the power to prevent someone from being a registered Republican, or for running under a party's banner (outside of being challenged in a primary, which doesn't seem to be happening here?)