Mineral spirits will not damage car paint as long as the paint on the car is fully cured and not freshly applied.
If you just had your car painted or have just painted your car and the paint on the car is still pretty fresh then the use of mineral spirits or any other thing such as nail polish remover etc could damage the car paint.
But as long as the car paint is fully cured on the car then the mineral spirits or other cleaning products should not damage car paint.
Mineral spirits can safely be used on car paint to help remove tree sap and clean other hard to clean grime off the cars paint.
I've used mineral spirits to clean my car and it never damaged the paint.
You can also use some rubbing alcohol or WD40 to remove grime or tree sap from your car without damaging the car paint.