General Discussion

Since they are the mechanism by which parties choose their candidates. The general election is a state function, not a party function, so there won't be separate lines for the general election.

I've been involved in elections in probably half of the states, one way or another. Laws vary somewhat from state to state - but they vary far less than you might expect. Your voter registration information, your voting record, and which party primary you voted in is public information.

Here's the request form for Texas - which anyone can use to request voting records. You may be surprised what information any person can obtain from a voting record request: chrome-extension://efaidnbmnnnibpcajpcglclefindmkaj/https://www.sos.state.tx.us/elections/forms/pi.pdf

If you don't want your party affiliation known, you need to ask for an issue only ballot (and skip voting in a party primary).