Ok, solved the problem. We do not use DNN's built-in user/session logic for our accounts. The original viewstateuserkey (as implemented in the default.aspx.cs) is the following:
if (User.Identity.IsAuthenticated)
{ ViewStateUserKey = User.Identity.Name; }

As we do not have a user.identity, the viewstateuserkey could not be used, and thus the viewstate was the same for every user. I have modified this ViewStateUserKey to include our unique identifier.

Regards

What do you mean that DNN requires a user to work? 

We have an external service serving information to our custom modules, and users must authenticate to this external service first (through yet another custom module). We could not use the DNN mechanism as we wanted to use the asp.identity framework.