Have you tried messenger.com from your browser?

Edit:

Just went on it. On a browser you have to enable desktop mode for login to show.

Also if you login this way and disable desktop mode it forces you out. If you reenable it renders the chat. Theres no reason the chat wouldnt work on Mobile desktop mode isnt using a different browser just lying to the web server and frontend JS.

Amazing. I already rarely use Facebook as it is. I might just outright stop since they are dying to infest your phone so badly.