In a misguided attempt to prevent automated logins, F-Droid’s forum, which is powered by Discourse, does not display the login prompt or otherwise layout correctly if it does not recognize the user agent.
I have written about this type of nonsense previously. The solution is to use domain settings to set the user agent to anything recognized by the server. WebView Default works well, although it discloses a lot of information about your device.
And, just like magic, everything starts working.