If you report what information you are looking to limit on your activity feed, we can help you to stop receiving new alerts for these. We won't be able to remove old information. If you'd prefer to work in private, please email email@example.com for further assistance.
Well, you should at least delete invalid links like deleted repositories and unfollowed users. Don't be another GitHub, which doesn't update links in the activity feed to, for example, renamed repositories.