I've been voting since the early 60s and for most of those years, I had been a registered Independent, but joined the pubbie party to vote in the primary {we have closed primaries in PA} against snarlen arlen.
We finally got rid of sphincter but now we have casey, a demonRAT no-show that never goes to work.
An Independent in PA can not vote at all in any primary for either party.
Actually here in Indiana I can vote in a GOP primary as an independent... but the GOP could protest my vote as not being primary loyal to the party. As an independent I could probably get past that since I’ve historically voted Republican. Were I to try to affect the Dem primaries not so much. Of course that means they’d have to actually protest my vote which is the gamble. Always made sense to just stay in and vote Republican... but now that I’ve reread the rule I might go Independent on principle.