Lists can already be hidden, but there should also be an option to completely hide your profile from the public.

Currently anyone can see your:
• profile picture
• username
• amount of games
• amount of wishlisted games
• amount of favorited games
• progress (breakdown of you game statuses)
• game activity
• ownership (breakdown of your platforms)
• genres (breakdown of your game genres)
• top developers
• top platforms

For more privacy, there should ideally be a public/private toggle for every one of these details. A shortcut to make everything private would also be appreciated. Making every detail private would basically mean that you don't exist on the website to the public.