Registering as an "Independent" party member doesn't mean you have no party affiliation; most 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!
LA Times had a good summary a few years back: https://www.latimes.com/politics/la-pol-ca-american-independent-party-california-registration-card-20180405-story.html
You don’t need to register with any party to show you don’t like R or D, do nothing or choose "unaffiliated if you want to be “little i independent”.
Examples:
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New York - http://ipny.org/platform.html
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Oregon - https://www.indparty.com/
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Illinois - https://www.iviipo.org/our-policies/economic-issues
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American Independent Party - https://en.wikipedia.org/wiki/American_Independent_Party