We have T-Mobile and they CAN block texts, they just don't want to.
DH had a "conversation" with them, that finally resulted in texts being blocked. We were getting "spam" texts (i had no idea there were such things!) and being charged 20 cents each for them. I know 20 cents is not a big deal, but imagine if you got charged 20 cents for every spam email? It's the principle of it. I don't want the spam in the first place, I certainly don't want to PAY for the bother.
Also, DD *does* have texting on her phone and we have a family plan; we share 700 minutes. So only "commercial" texts are blocked. We can still receive texts from DD and also from our friends. I have a couple of friends who are very into texting and send out mass things like "Happy Easter" (the most recent) and I don't mind that. But I'm not paying for spam.
T-Mobile tried to tell us they couldn't do this, but if you are persistent, their technology improves itself.