If the paint is stuck to non-painted plastic (textured or smooth), it'll eventually loosen up due to expansion/contraction, oxidation, or out-gassing of the plastic. In other words, it'll eventually come off. Sometimes, use of a pressure washer will help things along. Applied liberally,
M40 Vinyl/Rubber Cleaner & Conditioner will help to weaken the bond.
If the paint-blob is stuck to automotive PAINT, and the paint-blob is thick (and nothing in the chemical realm works)... Use a
plastic razor blade (or a brand new putty knife, taped with masking tape) to
push against the paint-blob. Again, liberal use of the M40 will help. This method is a long-shot, but give it a try.
If neither of these methods work, this one will:
Oh boy, I can hear the screams in protest of this recommendation already)...
1. Remove loose contamination (pretty obvious).
2. Wax the area with the hardest wax you can find (a paste carnauba works well).
3. Let haze, then wipe off excess residue.
4. Use a new razor blade. Rub the blade-edge across some rough leather (like the backside of a belt). The motion should be as if you were painting with a paint brush... Back and forth. This will fine-hone the blade.
Now, gently push the blade (at an appropriately slim angle) against the paint-blob, doing your best to avoid gouging the car paint (duh).
The wax coat is a barrier, and will allow the razor to ride upon it. Sometimes you'll notice the wax being scraped away. If that's the case. re-apply and repeat the process.
I've used this process dozens of times. A few times I did 'scrape' away a little paint, but it was not very noticeable.
BIG recommendation that you get the feel for the razor on a junk panel before you make the attempt on your ride.
FYI...
Before there was such a thing as over-spray clay, a company used this method (with huge success) to remove paint overspray from vehicles (primarily for insurance companies).
I used the method a couple of times to remove overspray, but it was too freaky for me!