Generally speaking, most people on the left talk about a certain number of ideas. For example, many on the left believe strongly in trans rights. They believe that trans rights are either being actively limited or are actively under threat by people they believe are trying to either get rid of them or force them back into the shadows.

So, when a prominent figure such as JK Rowling starts both talking about “protecting women” and the “trans mafia”, they become concerned about what influence she might have on the debate on the rights of trans people. They criticize what they believe to be false or harmful beliefs about trans people and believe that her words are actively doing harm by promoting those false beliefs.

People on the left generally do not believe strongly that “more discussion leads to correct beliefs”. They point to the many moral panics, bigoted movements, and real harm done to certain groups in history and do not believe that what some call “open discussion” has historically always led to the least harm.

People on the left generally do not believe that all discussion needs to be censored or tightly controlled. Rather, they view certain beliefs and viewpoints as actively harmful because they spread harmful beliefs about particular demographics. They believe that political discussion can, and does, go beyond what is useful or helpful sometimes.