In Texas you don't really register with one party or the other. Every election year, voters get to choose which primary they vote in.
^^^
We don't do party registration here. For purposes of getting on party mailing lists and being allowed to attend precinct caucuses and whatnot, it's a matter of which primary you vote in. If you voted in the Republican primary this year, you would be considered a Republican, be allowed to attend Republican precinct meetings and probably get spammed to death by campaign mailers for the next two years. Same for the Democratic primary. If you don't vote in a primary, you're treated as an independent.