This question is in reference to Atlassian Documentation: Set Your Profile Picture
If you search as an anonymous user for a word such as 'profile' you will get the user avatars returned. They cannot be seen or accessed, but the results are still returned and look messy at the top of the page.
I used to be able to ask users who uploaded profile pics to remove them, but that is no longer an option (6.0.3).
View user profiles is already turned off under global permissions. Problem is not that anonymous users can see the profiles (they can't), it's that the registered user avatars show up in search (or more specifically placeholders for them do). I've not found anything that addresses that other than removing the user avatars... which you can't in v6.
I should have been a little clearer
In the answer I linked to, there is a link to an improvement request to stop user information showing up in search (that would obviously stop the avatars being shown as well). Unfortunately Atlassian decided not to proceed with that feature request because of "limited demand", but there is a similar request here: https://jira.atlassian.com/browse/CONF-1882 This has many watchers, many votes and what looks like regular and active user comments. You're clearly not alone in wanting this functionality!
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