Anyone registered to vote can choose a Republican or Democratic ballot. Many of the people on the Democratic ballot (in my area) are running unopposed, so it was a good opportunity to try to get the least crazy people on the November ballot. Also, the republican ballot has 13 propositions that are not on the Democratic one, so that’s your only chance to have a say in those (and IMO they are really really bad!)
In Texas, the main consequence is that you can only vote in that same party’s runoffs, but you’ll also get texts and mailers from that party. You can vote for whoever you’d like in the general election.