My AI took a peek at the GitHub repo to understand it better, and noticed the user ID is retrieved from the UserStatsReceived_t callback.
That's incorrect - the plugin actually ignores that event (typical AI hallucination...) It currently just logs to the console in that event and does nothing about it.
A potential fix might be to use the standard SDK function SteamUser()->GetSteamID() instead. This synchronous call should always return the ID of the actual current player, which would resolve the issue in Family Sharing scenarios.
This is what the plugin already does: it ends up calling SteamUser()->GetSteamID().GetStaticAccountKey().
So I'm not sure what the problem would be - perhaps there's some other ID we need to expose with the plugin, but I don't know what that would be - it probably depends on how all the server-side validation works. It might be a good idea to ask Valve for support.