Honestly, it all depends on your shoulder structure. If you have a tight acromion, heavy dips + overuse can really hurt you. On the other hand, some, like myself, can do them heavy and frequently and have no issues.
I prefer to do them second or third in a workout however. In my experience, I can still go really heavy with these when fatigued, so I like to hit the chest/shoulders/triceps with a few open chain movements (BB/DB) first.
I will occasionally use dips as my primary exercise, but I like to warm my shoulders up really well first. Not because I fear hurting them, but because I feel a lot stronger when I do. When doing so, I bang out a few mobility exercises, then do one or two easy sets of push-ups for 10-15 reps followed by some explosive push-up variations for several sets of 3-5 reps, then one or two sets of body weight dips for a few reps, just to work the groove, and then it's on.