"Using wrong pronouns is violence" is just one part of a general trend of excessive hyperbole in public discourse.
"There are downsides to keeping domestic animals as pets. Make sure before you take on a pet that you can not only care for its health but also give it a fulfilling life." But what we hear instead is "Pets are slaves."
"Sugary caffeinated soft drinks consumed in excess are bad for your long-term health." But what we hear instead is "Coca-Cola is poison." Substitute any food or drink whatsoever that someone disapproves of for any reason whatsoever; it's all described as "poison."
My purpose here isn't to discuss animal rights or proper diet, but to place "...is violence" in this larger context. Doing this is taking an aggressive stance that attempts to nullify all opposing points of view and force someone's preferences onto someone else. It can be successful ("abortion is murder" sure got a lot of mileage) or just annoying (think of how most people react when a militant vegan asks them how does their murder-burger taste?) or nearly comical ("taxation is theft").
There are two things wrong with it. One is, if the cola-is-poison viewpoint prevails in redefining "poison" to be "anything potentially harmful for your health if consumed excessively over a long period of time," what do we write on the label of the bottle of stuff that will kill you dead in a few minutes or hours if you consume an ounce of it? We can invent a new word that means actual-for-realz-poison, which the same hyperbolators will immediately appropriate as the new even-better word to describe their feelings about carbonated sugar water (or milk, or non-organic produce, or fast food...).
The second is, it contributes to the minmaxing on social positions that's stressing everyone out. Advice is phrased as demands. Correction is phrased as condemnation. People tune it out or respond in kind, so the purpose of the advice or correction is nullified. It's like a bad marriage where one spouse hesitates to ask "did you pay cable bill" because the other is sure to respond "you never trust me for anything!" But on a global scale.
For some reason we can't just agree "it's rude to disregard people's reasonable preferences in how they're addressed; and we can discuss what preferences are reasonable or not, and what is or is not a reasonable response to any such rudeness." Instead we have arguments between extremes. After all, if you've noticed, the real-world counter-argument to "using wrong pronouns is violence" hasn't really been "no it's not, don't be silly." Instead it's "gender affirmation is grooming." Being expected to pick which side is less stupid is stressful.