Phew that was one goofy bug to track down. There was a conflict between icon output across multiple plugins. I've fixed it in all of them and updated your install. The primary cause was CB Progress Field being output to registration and profile edit as it does an edit access check that was causing the privacy controls and field icons to cache their output too early. It required fixes in the following.
CB Conditional
CB Core Fields Ajax
CB Privacy
CB Progress Field
Also added following bug ticket for the issue.
forge.joomlapolis.com/issues/7124
Your install is already up to date with latest builds above and appears to be working fine now.