Hence, a simple privacy feature found in e.g. mastodon: allow users to check a box on pages to disallow search engines indexing them, including the profile page, post pages etc. Probably with the meta robots noindex tag. I dunno about shared posts; maybe disallowed posts could be removed from the render for well-known crawler user agents, or something.
However, this is a fairly rudimentary privacy measure that doesn’t prevent rude bots or web archiving services (which are also rude now) from indexing their pages anyway. So, at the cost of being inaccessible to guests, a privacy feature found in e.g. tumblr: allow users to check a box on pages to only allow logged-in users to see their profile and posts. I think this should also apply to shared posts, unlike tumblr which for some reason still leaks shared posts from blogs set to this mode. This mode would probably also have to disable the RSS feed.
There would then be 4 levels of privacy for pages: public, unlisted, logged in only, and private, which i think is nicer than only public and private.