So right,
The guy is the one who opens the car door because he is the one taking the girl out. If the girl was taking the guy out on a date than you could say that she should open the door
It’s normal for the one who is “hosting” to take care of all aspects that their hosting includes.
And as many posters wrote, it doesn’t have to be done in an untznius fashion. Most guys open it and then walk to their side of the car and let the girl close her own door.
Do you have a problem that it’s the guy who takes the girl out and not vice versa? Is that also stemming from the goyim? Is it too romantic?