YSK Registering as an "Independent" party member doesn't mean you have no party affiliation; some states have an Independent party who has a platform that you may or may not agree with!
It’s a common misconception, but if you registered "Independent Party" you aren’t “independent” you are a member of your state’s Independent party, who has a platform and agenda you may or may not agree with. What you actually want is called an "unaffiliated" voter status. The good news is, all you have to do is...nothing!
Picked some random states, they're all different which is also part of the confusion when citizens move. They may not record it for the state but can those in the state still register or join a party on their own? Issue would still exist if so.
People also just get confused by terminology and the mechanics and do it on accident, though much less common if state isn't including it on voter reg for sure.
The genesis of this post was a family member in a very blue state, who went to an ivy league school and is extremely progressive and was sick of blue/red and googled "independent party" in her state and when I sent her the party platform she was registered for she lost her mind.