Some of our users would like to hide their profile from users which are not friends.
Don't you think that such a feature would make sense?

No. All or nearly all information is in forum posts. Such a feature would mean all forum posts by members would be hidden from all other non-friend members of a forum. Discussions would have missing posts of what should be discussion. If someone wants their important information private, they wouldn't share it. Profiles also have important links like membership information and links to their content.

I think it's just meant to be permission to view their profile page. Yes I like the idea and not sure why there is a 'friends' feature without it.

From the profile it is just a lot easier to find someone's content, that's why some of our users asked me if there is a way to manage who is able to see the profile.