******* QUICK AND EASY SOLUTION FOR MUTING CAMERA SOUNDS *******
I think my post above is overlooked by most, so may I take the liberty of posting it again?
"I just checked out Camera MX and it doesn't make the shutter sound when taking a photo or a video (when you disable it in the app's menu), only a very quiet beep when stopping the recording of a video. The hardware button is something it does not support, unfortunately. @paulkreuzer : Camera MX doesn't require nearly as many permissions as Z Camera."
I posted this because Camera Zoom FX Free doesn't silence the camera, apparently, and readers of this thread get the impression that the only way is to root the phone, which is not true. Also I, for one, won't root until we get the how-to from the Fairphone team and others may not want to root at all. So for anyone in this situation, go try the app.
P.S. I am not in any way affiliated with Camera MX - it is free and doesn't show ads anyway. Other comments about free apps known to work welcome!