It is completely consistent with the first, and most supreme law ever passed by the newly created United States.
The Declaration of Independence.
The 14th Amendment provides in part:
"All persons born or naturalized in the United States, and subject to the jurisdiction thereof, are citizens of the United States and of the state wherein they reside. No state shall make or enforce any law which shall abridge the privileges or immunities of citizens of the United States;"
Most of the people who reside in Texas are citizens of both Texas and the United States. None of their privileges or immunities as citizens of the United States can be abridged by any act or law of Texas.
It would, of course, be impossible to secede from the United States and to replace the government of the United States with a new national government in Texas without violating the protections afforded to United States citizens as United States citizens living in Texas. However, if enough Texans favored the idea, maybe they could convince the rest of the country to amend the Constitution to permit a "secession." That seems unlikely to me, though, because very few Texans want to lose their status as United States citizens.
The question raised by this thread is sort of like the question of whether the rest of the United States could sell Texas to the Chinese or the North Koreans. It might sound like an interesting question, but brain cells shouldn't be wasted on it.