It depends on the layout of the campground. I never cut through someone's site. HOWEVER, we were in a campground that was a circle with rows of campsites within the circle. The bathhouse was in the CENTER of this circle. There were two ways to get there: walk a considerable distance around the circle to a entry road, OR cut through campsites. We decided to cut through the campsites.
A few weeks ago we were in a state park where the easiest way to get to the bathhouse was cutting across campsites. So we had a lot of traffic walking by us. We understood the reason so it did not bother us.
That was a lesson for us. We learned that some campgrounds are designed in such a way that traffic moves through campsites rather than around them.