First the valid point that cartoon makes: emotions and experiences are very important and should not be ignored. Very few people have the ability to express strongly-held ideas, thoughts, and beliefs free from emotion (i.e. tone) and asking them to do so is frustrating to them. Now for the problems...
Tone Policing Is Just Another Way to Protect Privilege
It could be, just like choosing vanilla ice cream over chocolate is just another way to express racism. Or sometimes, you just feel like eating vanilla.
When all you have is a hammer, everything looks like a nail.
Does displaying anger/strong emotion distract from the issue? If the "issue" is one where facts and reality matter, then YES. There is no question that emotion interferes with the reasoning process. This is why the heuristic that people who display strong emotions are less likely to be thinking reasonably and, less likely to have their facts straight is a reasonable one. But as we know, most people are not interested in facts and reason, and strong emotion is more persuasive to them. This is why a handful of moms parading their children who are on the autistic spectrum around claiming vaccines made them this way is more convincing to many people than decades of research by the world's top scientists as well as formal statements by virtually all medical and health organizations.
No matter how emotional one might be, it does not change the facts. If the "issue" is the subjective feelings of the individual, then NO. If a person is sharing a subjective experience then their emotions are important.
"Tone Policing" The term "tone policing" has been around for a long time and is a legitimate fallacy (I need to add it to this site!). As Wiki defines it...
Tone policing (also tone trolling, tone argument and tone fallacy) is an ad hominem and antidebate appeal based on genetic fallacy. It attempts to detract from the validity of a statement by attacking the tone in which it was presented rather than the message itself. Everyday Feminism is attempting to redefine the term to support their ideological agenda. It has nothing to do with minorities, the oppressed, or feminism. It can certainly be used against these groups, but it can be used fallaciously BY these groups as well.
Right off the bat this cartoon got it wrong... the argument made by Person 1 about the 1200 Aboriginal women being murdered was responded to
with complete agreement . Person 2 made no attempt to "detract from the validity of a statement." The suggestion to tone down the rhetoric, "e.g., 'our bullshit government'" was most likely an attempt to help the arguer appear more credible - NOT to shut down the argument.
Strong emotions are the fuel behind many of our most problematic cognitive biases, which are responsible for us ignoring facts and distorting reality. At the same time passion is a powerful force for change. The key is to develop the passion as a result of the facts and not start with an impassioned opinion based on subjective experience and cherry pick the facts that support your view.