They can still get your texts and contacts and call history from your car though. In many cars it syncs.
Source? If so, that's a privacy boon for CarPlay and Android Auto.
Then why does iOS warn me that my car will receive data from my phone when enabling car play? Does this just mean the screen, or does it get the texts/calls too?
Several of those can be limited to specific applications, e.g., by setting the $DISPLAY value (X11). For remote desktop that's a bit more challenging but can be managed to an extent using Group Policy settings under MS Windows: