Almost 150 people have reported this exact problem. Of cours not everyone experiencing this bug has made it to these forums yet so just imagine the amount of people suffering from this bug.
10 days after launch we've had no official reply from EA yet. It's a game breaking bug not allowing people to enjoy the game or save their progress. It's a shame there is no information about an update or fix yet, even though many people in this topic have helped to narrow this problem down and find the cause of it all.
For everyone with a ps4 not responding to anything anymore... Don't immediately pull out the power cable. Press and hold the touch button on the ps4 itself for 15 seconds and it should also turn itself off.
For now, if you do still want to play and minimize the chances of crashing... Strip down your car and remove most visual customization from it. (My car has just 5 aftermarket parts equipped) Also don't use a (complex) wrap and just paint your car in one color. After you've done this, quit te lobby, go to the main menu and load up your game again.