Hi there,
We got a similar issue from another user a few days ago and we found the reason was theme conflict. The quickest way to figure out if something is interfering is to test for a theme or plugin conflict. I know it’s less than ideal, but could you please try the following:
Temporarily deactivate all the site’s plugins except for Jetpack and clear your browser’s cache. Then check visibility settings again. If it’s working, then we’ll know that another plugin is conflicting here. You can re-enable your plugins one by one, trying visibility settings in between, until you find the one causing the conflict. You can leave it disabled or reach out to the plugin developer for a fix.
If disabling plugins doesn’t help, it may be the theme. Temporarily switch your theme to a WordPress default theme like Twenty Twenty. Then try visibility settings again. If it works, then you know it’s a problem with the theme, and you can reach out to the theme developer for a fix.