The fact that the parties have privileged access to the ballot is arguably not a partisan issue.

In many places, the support of a recognized party dramatically lowers the requirements for getting on the ballot. In my state, by as much as a factor of 3:

https://ballotpedia.org/Ballot_access_requirements_for_polit...

Not all primaries are partisan.

As a non-Republican, non-Democrat, when I voted in the last primary, there was exactly one referendum on my ballot, and nothing else.

I was also the only person on the nonpartisan register at that time of the morning. They had to crack open the shrink-wrap on the ballots just for me. I imagine that not many other people would bother to drag themselves in to the polling place for that one issue, were they not also choosing candidates for one party or the other.

I can think of non-partisan objectives, like pushing for open primaries in all States, and allowing for same day registration.