That makes me curious if there's been studies on the typical percentage of people who register with a different party than the one they typically vote for. Especially comparing closed primary states (like Pennsylvania) to open primary states. Closed primaries clearly disincentivize registering independent but I could also see people believing it's advantageous to cross-register, especially when your preferred party is incumbent or when in a state that consistently votes the opposite way as you.

Sadly, that doesn't matter to them - at least from what I've seen, the predominating narrative among rightists and "centrists" is that he only registered Republican to sabotage/protest-vote in their primaries, and that therefore he's actually far-left Antifa did it.