Option to prevent anonymous users (incl google) to view user profile details (changes)

Currently when someone changes its user profile, and when there are spaces available that anonymous users can use, those anonymous users can see the user profiles changes in the list of recently changed pages. They are able to view each user profile.

Sometimes this is good, but sometimes the user profiles contain information that should not be visible on the internet.
I think it is a privacy issue, because when visible for anonymous it also means it will become googleable. User should be aware of this.

I really would like this to be configurable, so that we can turn this behaviour off. May be each user should declare himself that it is allowed to publish the user profile to anonymous users.

We were confronted with this issue when opening up one space to the anonymous world.