No. There's no evidence that baby oil products hurt the paint on your car.
According to this post on Topspeedracer.com, it is a common misconception that silicones and petroleum contents found in car care products are harmful to tires, dashboards, paint, etc.
The petroleum contents you are referring to are known as petroleum distillates and they come from the distillation of petroleum crude oil. Thousands of products you are familiar with such as baby oil, Vaseline, and ChapStick are actually petroleum distillates.
Tire shine products from established companies such as STP, 3M, and Meguiar's are no more harmful to your tires than ChapStick is to your lips.
These companies use a multiple distillation process which removes impurities and toxins. Their final products are safe for human handling and use on your car.
While there do exist some petroleum distillates that can be very harmful such as gasoline and paint thinner, one simply cannot label all petroleum distillates as either good or bad.
All paints are made up of three ingredients: binder, pigment, and a carrier agent.
Pigment, or tint, is self-explanatory-it’s the color you see.
Binder is often referred to as resin, and it can be helpful to think of it like tree sap, that thick, sticky hydrocarbon liquid that hardens when exposed to air.
And carrier agent refers to the solution that the resin is suspended in. It keeps the binder in liquid form until it is applied, at which time it either evaporates or chemically bonds to the surface of the car.
Learn more about automotive paint at Hotrod.com.
Check out The Ultimate Guide to Protect Car Paint From Scratches from Cowlesproducts.com.