MMS yes, by deleting all the APN profiles. Always did it since 20 years ago
Can disable SMS sending by changing the “SMS center number” but I don’t think can disable reception
Luckily in my country the carrier in the early 2000s they decided to scam users with MMS and the “internet button” nearby the “OK” button and not with the “SMS double dip” where both sender and receiver would be charged for texts - too prone to abuse from assholes with large plans
“Internet button scam” explained for young people: in the early 2000s some carriers charged 1-2 euro each time you started an internet session. This for two main reasons:
To block new chat apps. We had “jar” apps like ebuddy, IMO or jacksms that could let the user chat spending much less. They were super optimized for data saving and even at the astronomical 20 euro per MB that they were charging at the time, it meant a chat session with a friend would cost 8 cents instead of 3 euro of texts. I would make two short calls to my friend, it would mean “go online and check the chat”
Get free money from people with fat fingers. Opening the browser would immediately charge the user 2 euro. There was a competition between phone makers to place the “internet button” in the most asshole position. Nearby the “call” button, or as a dynamic button, like at the home screen, the “ok” button would open the internet, while in the menu would be “ok”. I had a Motorola where they placed it in the middle or the D-pad and I always accidentally pressed it. This could be mitigated by avoiding the purchase of a “carrier branded” phone because it could be toggled off. If you bought a phone with Vodafone branding instead every button had a way to let you spend money