You must have an account to perform pretty much all actions on a site such as posting. Therefore, allowing users to post without an account doesn’t exist.
Edit…
If you need some level of animosity you could use anonymous posting? Caveat is that it still needs users to sign up.
Or change the site setting hide user profiles from public and hide it from user preferences with css so users can’t unhide themselves? But as with any css a user can find a way around it eg. Using safe mode.
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