Well, apart from the alarming ease with which the writer is happy to discard freedom of speech, I would start with how the statement relies on imprecise concepts to make its point. Obviously, I understand in broad terms the message, but actually I don’t precisely know what is meant by “denying other people’s reality”.
What is other people’s reality exactly? Is it different from reality?
If I don’t agree with a belief (assuming this is what is meant by the above) does this amount to denying it?
The sentence makes sense apart from this nebulous phrase which is doing all the heavy lifting.
If we don’t even understand or agree on what this is, how can we assess whether it is serious enough to warrant policing speech?
But this sort of thing is par for the course in this ideology. It’s how I often find myself spotting examples of people who seem to be ardently for the cause saying things that fly in the face of its ideological underpinnings. Most people simply don’t understand the arguments when you dig into it, while a small number are consciously using obfuscating language.