Fyi some auto makers will "disable" the data collection and upload, if you call them and tell them to for your vehicle. Now whether they actually are disabling it is another story entirely...
There are likely ways to "root" your car and take a look at exactly what is going on but I have no clue how.
An independent mechanic would probably do it. The dealer probably wouldn't.
Disabling the modem would make any features that rely on Internet stop working. Could mess up the infotainment system. If the wire that powers the modem also powers the radio then you could lose that too. It will take trial and error to find the right wire and it's different for every car.
That's why I suggest using a switch instead of cutting it out completely, so if it breaks something you can turn it back on. This also helps to retain the value of the car since the next owner probably wants the modem on.