You cannot stop the collection. It ALWAYS collects. It may not transmit, even if connected. For example the black box in many cars is really an assortment of ECUs that contain fine grained historical data. It does eventually roll over and get replaced but the data is there.

For example there are public cases you can find where the police, not even needing a warrant, were allowed to dump this data off of a rental vehicle that a suspect, not convicted just suspected, was thought to have been in. Of course the copaganda story showed that they the used this data which was mostly location by gps and speed by the wheel sensors and gps to get a track of everywhere that vehicle had been in the last 6 months. Every person who rented it and drove it somewhere had their privacy violated. But I guess that's normal now.

The infotainment systems are the biggest jerks for data storage as they're just mini generic computers today with lots of storage.

To stop wireless transmission you can remove the sim card from the modem. Many vehicles won't work or even start if the modem is disconnected (unplugged or unfused). A Nissan for example will drain its 12v battery overnight trying to find the modem if it is unplugged. But if the sim is bad or disabled, it will try and fail to communicate, then retry later which won't kill the battery.

You lose a lot of convenience and the data is still there. So the answer is basically you can't drive a new vehicle without it violating your privacy with collection. You can only make the wireless transmission more private or disabled. I suppose you could buy a scanner yourself and before you leave the vehicle, factory wipe all ECUs. But even then you'll need to enable them for emissions testing and such if that's in your area.