So if my kbin account is in kbin.social, I am not able to login in the app at all?
That's correct, for now at least. It's not a limitation of the app, but that the API has not been enabled (by the kbin.social admin) on this server yet. At the moment, kbin.earth might be the only server that has working login functionality, but you could try some of the other API enabled kbin servers, it'll pop up an error if they don't work. See my related comment here.