Attaching two images of what I'm seeing. The first is right after opening the user's record for edit - the field shows permissions to the right with a black icon, and black text.
The second is after choosing a new privacy setting for the field - it changes color on the icon & text to grey, and the privacy setting is never saved on the back-end.
Changing front-end privacy on any field for any user works fine. I'm using the default Isis template for the Admin panel. I had CacheCleaner (plugin from Regular Labs) installed, but deactivating or uninstalling it doesn't change the symptom. I am using a RocketTheme Gantry 5 template for the front-end, but as indicated privacy changes work fine using it. I have RokBooster installed, but disabling it doesn't resolve the issue.
I see the following error line pop up in the Development console for the browser when attempting to change a privacy setting:
jquery-2.2.4.min.js?v=5eb7f75c6a9b7577:1 POST
www.my-domain.com/index.php?option=com_comprofiler&view=pluginclass&plugin=cbprivacy&action=privacy&func=save&privacy=af37fb86108da03f15ab26c8e56eaf62&Itemid=305&format=raw
401
That makes it look like there's a permissions error with the attempt to edit the privacy field for that data field (a 401 result), but it's just a guess. I am using SSL across the entire site, for all pages (self-signed cert on the server).
I unpublished all non-core CB tabs, with no change in behavior.
If it was a server setting, it should be blocking front-end changes along with back-end changes (both use AJAX), but it isn't. I'm at a loss for why it is happening.