If you do not want to claim a party affiliation, do not vote in the primary. Vote only in the general election. This way everyone gets what they want. The political parties get to choose who they want to represent them in the primary and find out who their members are, while voters get to choose across party lines to vote for whoever they want in the general election. Parties wax and wane, which is beneficial.
Parties are the lifeblood of our republic.
They develop platforms and issues. They encourage, recruit, train and support candidates and campaign workers. They educate voters regarding the electoral processes, issues and candidates. They provide the interest, creativity, energy, resources and debate about issues and candidates. Unorganized individuals can't.