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.

Only which primaries you can participate in. It doesn’t require you to vote in any particular way in the actual election. The public voter roll will show which primary you participated in, but your vote in the election is secret. So anyone who says they checked and confirmed their vote was counted wrong in the election is full of shit or confused by the public voter roll’s representation of party selection during primaries.

edit 1: I think Texas Standard did a nice job explaining it.

edit 2: The Texas Secretary of State office has a good FAQ, too. Some other interesting points in there that I didn’t know about. Specifically, that signing petitions for candidates also locks you into their party’s primaries (if applicable) for that year.

6. What if I signed a petition for a candidate for a place on the primary ballot?

If a voter signed a candidate’s petition for a place on the primary ballot, that voter is only able to vote in the primary, or participate in the convention, of that candidate’s party during the voting year in which the primary election is held. For example, if a voter signed a Democratic candidate’s petition, that voter is ineligible to vote in the Republican primary or participate in a minor party convention. (§172.026).

7. If I signed a petition for a candidate for nomination in the Libertarian Party or Green Party, can I still vote in a primary election?

No. If a voter signed a candidate’s petition for nomination for the Libertarian Party or Green Party, that voter is ineligible to vote in a primary election or participate in the convention of a different party during the voting year in which the primary election is held. (§§172.026, 141.041).