There's been some interesting threads about stylometry over the years [1]. The top link was quite decent at unmasking HN alt accounts with basic ngram analysis whipped up in one day [2].
It makes me wonder if we could use non-instruct LLMs to slightly alter the wording of text while keeping the meaning the same meaning. Perhaps by using perplexity or some other metric. I don't know, maybe you compare the distance of the "meaning" vectors.
You might also want to have some "style" vector associated with each pseudonym. For example, I might want it to produce british english under a certain pseudonym, and simulate an ESL speaker under another.
Essentially, you would want some way of re-styling text. The basic way to do this would be to run the same sylometry tools the hunter uses and manually make synonym word/phrase subsitutions to lower your similarity.
It's a cat and mouse game, but I think the mouse eventually wins. Consider a program that translates your english writing programmaticially into a low-entropy symbolic form and then translates them back to english in a procedural manner. Basicially you design an intermediary language that cannot contain style. It would be boring to read but it would remove all the style.
I still think people underestimate the power of even minor inconvenience. While you can't just click a button to reveal all pseudonyms of someone (e.g. you need to download some obscure tool or even perform statistical analysis yourself), I think this provides significant (and surprising?) protection for pseudonymous individuals, I'd say even (although to a reduced extent) for sophisticated threats like state-level actors. I hope LLMs continue to be unable to do so for the near future (I just tested and LLMs can't do it with a simple prompt).
Which is why I think privacy safeguards still work quite well even while being technically mostly bypassable.
So probably tools like this should be kept private if possible.