In this example, the 16x16 texel mushroom sprite has been scaled up to 17x17 screen pixels, and so the snapping happens differently from one part of the image to another, creating the ripple or wave that stretches & squashes it as it moves.
So, the trick is to adjust your camera size/field of view so that your assets' source texels map to an integer number of screen pixels. It doesn't have to be 1:1 - any whole number works great:
1:3 Scaling