No, you don't have to. Android Automotive is the base OS. Manufacturers can opt in to offer Google Automotive Services (GAS) which are a bunch of Google apps on top, which you do need to sign in to use.
Aw your car was suspended for abuse? Follow the FAQ link which turns into a recursive hell hole with no one powerful enough to help you when you eventually stumble on a human.
Dystopic action-comedy potential: a White House Down style thriller, except one of the key plot points is the villains immobilizing the fleet of Presidential vehicles by getting their Google accounts banned with fake copyright claims.
