I confirm that I have something similar. With the default installed version of Cheese on Zorin OS 17 Core:
When you open the app, there is a strange "loop" of the first 1 second of whatever Cheese "sees" via your camera. Dropping the camera resolution to 640*480 works around the problem...but you are in a lower resolution, which is not ideal.
I didn't try taking a picture or video clip to see if it worked.
I removed Cheese via Software, then re-installed the Flatpack version (also via Software).
Cheese works like a champ now, and at full resolution.