I’m cross-posting this issue from a repo that documents issues we want GitHub to notice and add/fix/remove/etc.
I’ll just repost the main issue and basic solution here for visibility
The Issue: Hiding Repos and Contributions
The main issue at hand is the profile page / feed, which can be found via Google. And for a variety of use cases (listed at the end of the original issue), you may not want every single contribution / repository showing up on your profile. The way this could be done is to give the feed / profile page options as to what shows up.
Doing any of this would be similar to having an unlisted video on YouTube. Repos and contributions are still public and linkable but they are no longer seen on your profile and no longer searchable by search engines.
A Basic Solution
For the feed, the minimum viable option would be to exclude repos by name as well as by type of contribution (issue, repo created, org created, etc).
For the repo page, it would be similar but you would only exclude unlisted repos. You could also specifically exclude forked repos