I am sorry as I do not know the exact steps that caused this issue. It all began when I was having trouble with Brave Sync (nothing happened when I had entered the correct words into the box and pressing sync, but I eventually got it working after an hour of fiddling). Just after I had gotten Sync to work according to a tutorial I found in these forums I found out messenger.com stopped working. At some point I also reinstalled Brave on both of my computers.
What it looks like:
It happens everytime I try to open messenger.com, on both of my computers, both on Brave running Windows. The website works on other browsers.
I have tried clearing my cache but that did not fix the problem, odd is that it happens on both of my computers that are synced together, not just one. That might be a hint to problems with Sync (bookmarks sync fine).
Operating system and Brave version:
Main PC: Windows 10 Home 64-bit (10.0, Build 17763)
Brave Version 0.65.121 Chromium: 75.0.3770.100 (Official Build) (64-bit)
Laptop: Windows 10 Education 64-bit (10.0, Build 17134)
Brave Version 0.65.121 Chromium: 75.0.3770.100 (Official Build) (64-bit)
I can also extract more info (code etc) if needed, just tell me 
Would love to have this fixed.