What you have pointed out, accurately, is the path that people can take toward radicalization, especially when they feel threatened, or afraid. That J.K. Rowling - an abuse survivor who has publicly struggled against misogyny throughout her career - has fallen down the anti-trans rabbit hole is disappointing but not surprising. This does not, however, justify or excuse her ongoing public vilification of trans women. The thing is, bullies are almost always hurting too. They make themselves feel better by finding someone who they can hurt...someone more vulnerable than they are. I can understand that and even feel sympathetic for the bully, but I'm still justified in my demands that they stop bullying me. If Rowling's transphobic actions are in fact just manifestations of her anxiety about the patriarchy, she needs to direct her efforts towards the actual source of oppression. And we need to hold her accountable for the harm she does when she acts the bully, and punches down.
The crucial element missing from your analysis is the role that power plays in this particular dynamic. Trans people comprise a vanishing small minority of the population who are far more likely to suffer from abuse, assault, discrimination, and violence than almost any other demographic. Trans feminine people like me experience all of abuses heaped upon cis-women, plus transmisogyny, plus all of the abuses heaped upon trans people. Joanne Rowling, on the other hand, is one of the safest, most influential and powerful people on the planet. This kind of "both-sides-ism" doesn't go down well when my side is existentially threatened, and the other side isn't. Combine the voices of every trans person screaming for help right now, and we still reach fewer sympathetic ears than she does with a single tweet. In terms of relative power we are ants against a giant. It's not like we asked for her attention. We were just existing, and just that - our existence was sufficient to provoke her outrage.
We ask so very little of cis people: treat us as our affirmed gender, call us by our names, allow us autonomy over our own bodies, and allow us to share the world with you as feeling human beings. The only thing this costs cis people is their biologically essentialist worldview on sex and gender. And the thing is, that worldview has been used to justify and uphold patriarchal oppression for centuries. Being "gender critical" ultimately reinforces the systems that are used to oppress all women.
In the wake of the most recent US election, as I fear for my own life and those of my loved ones, it's pretty hard to read an article whose core thesis is: "trans people shouldn't be so upset about transphobic abuse from one of the wealthiest and most influential women in the world, because she is hurting too." Lecturing vulnerable people to be more understanding of our abusers during the moment when we are (correctly) feeling more vulnerable than ever betrays a degree of unexamined privilege that I can't even imagine.
