I just set up a whole bunch of log in services on my self hosted instance. Level of difficulty varied with the various services. Generally, the ones I use were pretty simple.
I use google all the time and set up that log on service right away and use it myself. I recently set up github log in and that was easy but I use github. I recently set up Discord and that was easy but I had a Discord channel. I recently set up X (twitter?) and that was kind of a pain (but I don’t use it)
I did not set up facebook because I don’t use it and don’t have an account and really didn’t want to set up an account. That said…
You obviously use facebook so my gut instinct is that it should not be difficult. There is a guide with step by step.
If a person on your facebook group follows a link you post, they should (?) be able to just click one button and be logged in. They will need their credentials (user and password) the first time but after that it is literally one click.
The reason I put a question mark above is because, like I said, I didn’t set up facebook log in service. But… every other one I’ve set up works just as I’ve discribed.
I’m not sure you are going to reduce friction much more then that. You post a link on your facebook pages. Follow this link to the new group interface, it has a lot of new cool features. They follow the link, land on a sign up page, click facebook log in (or whatever it says) and they’re in.
As Todd said above, the google doc idea seems redundant to me as well. Discourse’s log in and sign up works really well IMHO.
Let folks know you are not abandoning them but all the new stuff moving forward will be over there. Maybe create or pick out one of the some what simplified themes available.
edit to add:
I just read your posts in the facebook log in topic. I’d still try to get it set up. If it breaks in awhile, hopefully most will have signed up