We don’t have an “Independent” option in Texas. At a primary election, one either votes in the Democrat primary or the Republican primary and that makes one either a Democrat or a Republican on the record. The person’s voter card is stamped Democrat or Republican when the person votes in the primary. One can think “I’m an Independent”, but the record and voter card shows either Democrat or Republican.
Not exactly. Whether the card is stamped with "Republican" or "Democrat" we can still vote in either primary.