Having been in both situations I have become heartless.

As a tank no DPS let up for me so I had to learn to deal with it. There wasn't an excuse, on PLD and WAR.

As a BLM or any other dps. I maximize my dps as much as possible. If the tank can't keep up then there is a problem and more often than not it has to do with rotation. Now low levels <30 I can empathize with Warriors and <26 with Paladins but no Shield Oath, you're just being lazy if you can't hold threat. I still have never used quelling strikes on any dps class.

As a Healer I have let tanks die, dps die and died myself due to either DPS being jerks, Tanks not doing their job, and me getting cocky.

Healers need tanks, tanks need healers, and dps need tanks and healers to be at their best.

The only actions you can control are your own. So why worry what buff another class is doing when your priority should be maximizing your ability to do your job.