Erik, I hate to be the bearer of bad news...
To fit 35's on our rigs, you'll need to do a bit of work. A 2" body lift and 1.5" wheel spacers and trimming.
A Titan swap or drop bracket lift will also do it but that's major $$.
The rubbing your experiencing is the tire is just to big for the wheel well. The inside edges are, most likely, rubbing against frame. I'm sure they are hitting the plastic too but that's not where the problem is. Wheel spacers will fix this. By using wheel spacers you'll have pushed the wheels out, away from the frame and, unfortunately, lined them up with the fenders. A body lift will raise them up further out of the way. A body lift will raise the top of the fender but the rear of the front fender doesn't go anywhere.
You'll also need to trim about 2" out of the back of the front wheel fender metal (in front of the front doors)
