After extensive work from the Google Hangouts team and the Firefox WebRTC team both, the consumer version Google Hangouts and the enterprise version Google Meet, are working in Firefox with no plugin required thanks to WebRTC!
How we got here
Turning off the NPAPI support in Firefox 53 resulted in the Google Hangouts plugin not working anymore. Unfortunately that meant that Firefox users could no longer enjoy Google Hangouts or Meet.
Google Chrome users could continue to use Hangouts and Meet without a NPAPI plugin, because the Google Hangout backend service had support for a flavor of WebRTC only implemented in Google Chrome. But that version was not spec compliant and was thus never supported by Firefox.
It took a considerable amount of effort from the Google Hangouts team to update their backend service to the latest version of the WebRTC specs to support Firefox. At the same time the Firefox WebRTC team implemented a bunch of features to support large scale conferencing for Google Meet.
In fact Google Hangouts, the consumer version, started working with Firefox 56. Now with Firefox 60 we were able to ship all the required features to also support Google Meet.
Thanks to all the hard working people involved in this project and resulting in making the Open Web a better and safer place from today on!