Are you sure you have to disable it? Many players will prefer to use fullscreen even if there are a few weird pixels.
There’s a good discussion about this topic here:
One suggestion made there was to increase resolution and then zoom the camera, which I think might help in your case (no need to scale up the assets, just the game resolution + camera zoom).
It is hard to see in the screenshots, but I still suspect that the player sprite might be on a non-integer coordinate. If you are using movement behaviors such as Top-Down Movement, then the player will move with floating-point accuracy regardless of game resolution. So for example the player X coordinate could be 12.5, or 12.00000123. If this happens then you’ll see warping on the player sprite but not the background, and should be fixable by restricting the sprite to whole coordinates.