Brexit showed us that situation like this the 'bigger person' in the conflict will try not to starve millions of people to death and will not simply cut them off. We as individualise would surely like to see Brits/Texans suffer all the consequences but politicians are usually more pragmatic than this and have to think long term. Turning Texas into 3rd world country wouldn't do any good to anyone. Blocking supplies as some sort of collective punishment would simply be immoral.
Of course they are not going to secede but if they did they would still get all the supplies they need. Their economy would suffer greatly but they would just blame US and keep going.
The entire Ireland is in the EU already. Northern Ireland can access the single market without checks. The checks are between Ireland and GB.