I cannot open chrome on my son's phone without the funamo screen popping up and asking for my sign on. I have not blocked that site and have tried to add it to the white list, but to no avail.
The Funamo login screen you mentioned in your post has nothing to do with web filtering/website block. The website block is in the browser and it does not have option to sign in. Funamo by default does not block other apps so please double check your settings to see which settings might have triggered the blocking. If you want us to double check your settings, please send us a private email with your account info (email used for your account).
Whitelist is a web filtering feature and it has nothing to do with app blocking.