The problems seem associated with the privacy settings rather than the browsers per se. Epic Privacy Browser and Opera VPN are both cagey about sharing info with Facebook. There’s also a clear difference between the results from Chrome in ordinary mode and in Incognito mode. So it looks like Facebook rejects the widget if it’s unable to query the browser for the information it requires: i.e. something to identify who you are.
In that case, the error box is a sign that you’ve evaded Facebook’s evil eye. Wear the badge with pride!