Those are called closed primaries

If you want a say in the Republican pick that’s going to run to rep the R party, you need to be a registered R. Same if you want a say in who the Dem rep will be in the general

This only applies to closed primaries

This prevents sabotage from people from a different party voting for a weaker candidate to represent your party in the general election

usuallly, you cab change ur registration just before the primaries and then change back after.

I just changed mine to independent in CO. They let me choose which primary to vote in. No idea about other states.