Of course they should. Tip: Don't phrase "they should have some recourse" as a question, it just makes you sound uncertain and invites refutation.
What if you are pro trans people? In 10 years you can be prosecuted by it, if a new party is elected. It can have new 'standards'. You will not be able to contradict mainstream narrative. You will not be able to say anything against corporations and governments.
If you will do anything outside of 'boundaries' set by companies, governments you will lost your job, spouse will leave you, all because you wanted 'a better world'.
On one side of scales is a place of total invigilation, on the other is a place with internet trolls. Companies like meta and twitter are quite good in rooting our trolls. So the current situation is inconvenient, but we can live with it.
If we opt out anonymity then the overall result will be a lot worse than the current situation is.
But on the other hand, what should someone do if they are truly wronged by something like this? They lost their job, their spouse left them, all because someone decided to slander them under the veil of anonymity. Should they have any recourse?