Shoulders and dips

Dips commonly seem to be considered hard on the shoulders and it sounds like there's a lot of people who can't do them. Every gymnast, and everyone here does dips though. Why is it that so many shoulders don't seem to like them? Is it a mobility thing or are there anatomical differences that will prevent certain people from doing them? With the right preparation, could everyone do dips?

It's a very basic movement. Problems with dips are almost certainly due to poor mobility. 

The issue is that most people just do dips without any preparation. If you lack the mobility they can hurt you.

Basically you are allowing yourself to go into a weighted stretch at the bottom of the movement where you have not developed stability. Eventually this can lead to shoulder issues.

If you follow a logical progression of preparing the shoulder girdle and extending rom with strength (mobility) then dips should be no problem in time.

Push up progressions and lean progressions will fix this strength and stability issue. Planche leans will help your mobility too.