The paint on 'plastic' bumpers and trim pieces is, by design, different in composition. The trim really flexes quite a bit (from both temp changes and physical stress.) So, simply, since the addition of flex agents make a different paint formulation, one should expect different aging characteristics.
The fact that your white is likely a THREE stage pearlescent, just adds to the mix.
Odds are quite good that it all an oxidation issue. Is the car kept outside during the day?
As mentioned, start with AIO/PC#5 and go slowly, keeping the panel moist. AIO is only a chemical cleaner, but action of the PC/pad combo will do 'some' actual polishing.
If you don't see immediate results, it'll be time to cowboy up, and move to a polish that will actually cur the paint.
In my shop, we'd probably start with rotary/polishing pad/Meg's Speed Glaze.
Good Luck!
Jim