Can I hide my accounts that I already participate in, for a specific site?
For example, I'm in one where I don't want to make my accounts visible for others:
Or is this not possible?
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Yes, you can hide as many of your accounts from ordinary members as you wish.
There you can select which communities you want hidden.
Note that the hidden communities will still be visible to moderators and Stack Exchange staff. They will show up in your Stack Exchange profile with gray backgrounds. For example, this user has their "3D Printing" site profile marked hidden: