Political parties, rather than local governments, administer primary elections in Texas. In the past, Democrats and Republicans have overseen them jointly.
The rules in effect Tuesday are part of local GOP leaders’ decision to hold a separate primary from Democrats this year in Dallas and Williamson counties, leading to precinct-based voting. In previous elections, individuals could cast ballots at any vote center, regardless of their address, under a countywide voting system.
It’s that way for primaries. Technically, in the US, political parties are private organizations. As such they can set up rules how they want within certain confines. One of the big ones is the fact that the democrats don’t even have to listen to their base’s vote and instead rely on a separate committee to select their candidate. This caused issues for Bernie Sanders and should have been a wake up call for people.
Now that being said, you’re welcome to try to get on the ballot in the general election as an independent or another party but Americans are so myopic they only see D or R which is a whole different problem.