Like other posters have stated, the debates and animosity exists to a greater extent on these forums than it actually does in game. From my experience, when grouped in an instance everyone is paying attention to what they are doing, but START paying attention to their group members when they disrupt the flow. And by disrupt the flow, I mean not performing the very basics of their role. Tanks who can't hold agro, face AoE towards the group; healers who are not healing, or keeping themselves alive, and DPS with low damage, or failing mechanics over and over again. These are the things that stick out like a sore thumb because they destroy the flow of the run.
When tanks and healers don't DPS, it simply slows things down. Maybe it's my datacenter or server, but these wrestling matches seldom happen in-game for the same reasons. It is entirely possible that players are remaining quite instead of voicing their frustrations with healers and tanks who don't add to DPS, but it only goes to show that they can and will tolerate it because ultimately, the main goal is still perfectly obtainable, and griping in-game will only slow things down further.
Compromise is a double-edged sword. Even with change in game play, the current frustration will only shift. Change in gameplay like removing Cleric during instances won't solve anything and infuriate DPS healers even more. Other examples I thought of can all be contested in one way or another. I feel the problem exists partially with how healers are designed. They have the lowest requirement of all roles in order to get a clear, but have the highest requirement to perform optimally. Because of this, a healer who optimizes their toolkit is ALWAYS going to be the ideal choice, and the majority of the player base wants an ideal situation. It's just how it is.
If as a healer, are so comfortable that you can /follow a tank with SCH, or emote and jump around the arena, or go AFK. You're are not being courteous to the other members of your group. I've been the nervous healer, afraid to go into Cleric and these actions are unfathomable for me. I could hardly believe the video I saw. If you see me standing around, I might not be taking any action, but the brain activity is at lightspeed levels, evaluating the entire situation.
Players throwing their hands up at the group with a non-dpsing healer isn't doing anything to help the group or themselves, or the community. You don't encourage good play with crappy attitudes. Good play is encouraged by leading with example, showing patience, willingness to work with others, and yes, rolling with the punches. I've gained my confidence to DPS while healing by aspiring to be like those players, not those abandoning duties the moment things aren't going the way they would like it to.
Each player type is being selfish and hurtful to others. A problem with the community can't be fixed by the devs. It's up the players within the community to make things better on their own.