Anonymity, understandably, leads people to behave in more radical ways than they otherwise would.
On the one hand that's often the conscious intent of it, but it also subliminally influences people unintentionally, which is why masquerade balls had a certain reputation and why road rage leads to violent outbursts that people would never indulge in the case of foot traffic. It's also part of why X replies are so often snide, condescending or blatantly insulting.
In the case of online political discourse the predictable result is that people tend to adopt more extreme positions than they would under their real names, even if censorship and doxxing weren't issues.
Those extremist tendencies are, of course, exacerbated by the nature of social media algorithms, which reinforce priors and stifle inter-ideological exchange because everyone is being fed, almost exclusively, content from their own ideological camp.
All this creates irrational behaviors (as in road rage, masqueraded bacchanalian excess, or internet ad hominem) primarily because it removes a degree of feedback and renders a person immune to incremental consequences for his actions, i.e., it takes away error correction.
As long as the vast majority of our politics is conducted anonymously we'll be exempting ourselves from the error correction that naturally comes with having your reputation at stake when you make a statement - errors will therefore proliferate and we'll lose touch with what's truly politically possible.
It also invites leading a double life, where your political views are quarantined and expressed only behind a mask, while your everyday life bears no signature of your identitarian commitments. That kind of double life is not healthy and is psychologically unsustainable in the long run.
I don't suggest going public with all of your most extreme positions under your real name; that would be irresponsible. I do suggest engaging politically under your real name in much more moderate ways.
Keep your anon account and keep pushing the overton window. But also, start a totally separate account using your real name and engage in the discourse in a way that is as honest as you can manage without jeopardizing your livelihood or personal connections.
That would give you the error correction that we've been depriving ourselves of and it would force you to take a more realistic view of politics.
TLDR:
-Anon accounts lead to unrealistic LARPing and prevent us from correcting our errors, but are still useful in pushing the boundaries.
-Self doxxed accounts greatly limit what we're able to say, but force us to be more realistic politically.
-So you should do both; have an extremist anon account and a moderate doxxed account and push both as far to the right as prudence allows.