Please try creating a new account on app disabling your custom login .IT should , its just that when you login with our login form we authenticate the user to firebase as well to access the database hits and function the whole chat .
I took it out because it was causing mistakes. but I added the mail of Alex as an administrator in firebase, so he can add those credentials to that you can test it and see with your eyes self.
So this don't work.
One thing to keep in mind that user has to login with wplms front end login popup in order to make the chat work .
At first page load is user has not logged in before it wont work but on second page load it will work .Also as you are using bp single page it will work on that page only right now .
If you want it to work on all pages then enable global login from wp-admin -> vibebp -> settings.