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You can ask search engines such as Google not to index your account by doing this:

1. Log in through your server's website
2. Go to Preferences > Other > Opt Out Of Search Engine Indexing
3. Tick the box and click "Save Changes"

(If you're on mobile you will need to click ☰ to see preferences)

Bear in mind this method relies on search engines obeying your request. If you want to be absolutely sure a post isn't indexed, use a non-public visibility.

More info at https://fedi.tips/hiding-your-posts-from-search-engines-on-mastodon-and-the-fediverse