It's funny you say that, because last time I had a rental with Android Auto it would not let me even start it without allowing access to my contacts and other details. I ended up not using it because of that.
The normal car bluetooth systems on the other hand don't mind if you don't give them access to things, and you can restrict it to music and calls only.
Maybe they just want to facilitate you by letting you voice your contact and send message or call your friends by voice. I don't have a car with Android Auto, can you deny the permission?
I use LineageOS which has something called PrivacyGuard. I can give the app permission to access my contacts but then deny it at the PrivacyGuard level. I'm pretty sure that it just returns an empty contact list in this case.
The normal car bluetooth systems on the other hand don't mind if you don't give them access to things, and you can restrict it to music and calls only.