The trouble is, if the things are called as what they are, you cant say "both sides are the same". Because one side is promoting cruelty and the other is not.
> says things they don't believe to curry favour
If you do not believe that trans people should be beating up, but say so to look manly to your boss, you still promoted beating of trans.
In my time as a righteous woke progressive, it eventually dawned on me that the other side was just as likely to believe in the righteousness of their cause, even if I couldn't understand their reasoning for it. It also dawned on me that the righteous folks on the other side of the divide likely see my beliefs and the reasoning by which I arrived at them as equally baffling.
If both sides believe fully in their righteousness, and see their opponents as wholly unreasonable, then we will end up in a non-religious holy war.
The only way to recover is for both sides to turn down their righteousness.
One small step to do that is to at least try to understand--without agreeing--why the people with whom you disagree hold their beliefs, which ones are inflexible and which are mutable.