Does it hide my info from them, or is it just so I can't see them?
I assume the mute button will eventually hide the account's posts and comments from you so that you don't have to see them. But as you already figured out through testing, it isn't actually functioning yet.
Regarding hiding your info from them, it is technically impossible to hide your public information from a stalker. All the posts and comments are on the public blockchain. So no matter what the steemit.com GUI does, a stalker could get access to that information very easily. I think providing users with a false sense of privacy is far more dangerous than not providing any (illusions of) privacy at all. So I don't think steemit.com should make it appear like they can hide a user's posts/comments from some other user that wants to see them.
That means it is very important for each user to keep this in mind before posting any information in a public forum. Don't post any information in public if the benefits of posting do not justify the risks of that information being used by bad people to hurt you.