>You could say you should criticise
I think the problem begins with the notion of should. And more broadly the notion that people have obligations. On top of that, people use the word should in a lazy manner. They don't want (or are incapable) of having a (significantly) deeper discussion on the issue - it takes a lot of work. To avoid that mental burden, shoulds come out.
Note, I'm not merely referring to your use of the word, but the larger idea that both sides have. Take this:
>but the problem is not the people who try to tone police you, it's the people who don't like your tone and don't criticise you for it - they silently just ignore your cause or vote against it.
As a general rule, when someone who thinks differently from you starts using the language of obligation, it will raise the defenses on the other side. The expected outcome is one of fight (counterargument, or merely raised voices), or flight (the behavior you describe).
There's likely a hidden obligation implicit in your comment. That I am somehow obligated to learn about wrongs being done to others, and obligated to help them (via voting, activism, whatever). And so the tower of obligations gets higher and higher.
In the last two years, I've read 3 books on effective communication, and they all describe this - one goes all the way and suggests you stop using words like should. Others are more nuanced but are saying the same thing: As long as your posture is that of "I know what's right" (which "should" automatically confers) vs "Let's explore and see how I might be wrong", you'll have this problem. (Internally you may be open, but what matters is your showing it - often the outward posture is different from your inner state).
In my experience, and in the experience of the authors, the behavior you describe is what is to be expected. So labeling them as the problem may, on some higher plane, be correct. But if your goal is to actually effect change instead of categorizing, the approach is ineffective.
The books suggest the reader try to be above all of this. They urge the reader to ignore the tone and focus on the message. But they also emphasize that expecting others to reach this level is expecting too much.
BTW, lest I be misunderstood, neither I nor the books are saying there isn't anything like an obligation, and that you should not have shoulds. Of course everyone will have them. The key is to realize that your set of shoulds will be incompatible with others. You could have a long, multi-day conversation with the other to align your sets, but if you just change the style (and tone) of the conversation, you won't need to.
Tone policing is a broad concept. For some who do it, it is very sincere advice. For others, it is a way of not dealing with the issue. Don't fall into the trap of lumping the two crowds in the same boat.
Finally, there's another reason people silently ignore or are turned off from aggressive tones. Many activists have the mentality of "Always find ways not to be ignored" which often translates to "Shout louder and be in their face" (literally have heard some say this). Their whole strategy becomes one of "Escalate till you can't be ignored". This rubs many (most?) people the wrong way. Without even knowing anything about the subject at hand, a lot of people will automatically switch to "Oh yeah! Let me show you how well I can ignore you!"
There's a maxim in the field of negotiations: The more pressure you apply, the stronger the wall the other will build around themselves. This dynamic is entirely independent of the message. Their advice is always what you may not want to hear: Change the posture (including the tone).