When this happens, Firefox has been updated in the background & the non-updated parts that're loaded into memory attempted to load one of the updated parts & found that they were no longer compatible, causing this message to appear.
At this point you HAVE to restart Firefox in order to be able to use it, no way around it. Soooo very fun on Mac & Linux since both can update in the background. It's also possible to have this happen on Windows, but it's far more rare as it seems to require having multiple different instances running at once.