I would gently point out that "aggressive cancel culture and violently insistent 'safe spaces'" has been the right's agenda for decades. It still is - despite popular opinion, most efforts to ban books and ideas are still coming from the right. Removing LGBT books from libraries and protecting children from (the nonsense term) "grooming" are violently insisting on safe spaces. But safe for whom? Being safe from the things they fear is the only possible choice. Safety from the things others fear is an alien concept and restricts them, which is unacceptable.
The problem appears to be that in-groups t see actions against others as normal and actions against themselves as inexcusable. Being in power means you don't have to have empathy. Fish don't understand water.