It never others me if a healer doesn't DPS while I am in a dungeon, mainly because I am not a tank in EXDR. However, what does bother me is when I am doing dungeons for say an animus book and I am clearly marking the target, yet the bard is sitting hitting every other mob except the one I target.
Stone Vigil is already a bitch sometimes; I don't need an already long dungeon inflated to an hour. True story. Healer was DPSing, though let me died quite a bit, the bard refused to target the target I marked (Was only a level 42 bard, so don't give me crap that she was overgeared, because she was not), and when said bard died, she didn't use return. She instead waited for the healer to revive her, especially after party wipes and had the weakness debuff. Then, during the final boss, proceeds to say "Gotta go, but I will keep my character here" and then dips out. Also, people still don't know how to dodge the AoEs in that dungeon.
What a terrible dungeon run that was. A decent dungeon ruined by lazy folks.