Google Calendar RSVPs in Fastmail
I have found very minimal information about this so I thought I'd post my experiences and solutions so far.
I ditched Gmail and went to Fastmail and generally LOVE it. The ONE caveat is that EVERYONE uses Google Calendar, and I have a tons of shared Calendars for bands and such, so ditching google Calendar is NOT an option for me. If someone sends me an event and I RSVP from the email using the top set of response buttons, the sender does NOT see my RSVP. I've found 2 workarounds that have worked so far for me.
Do NOT click the 3 big obvious RSVP buttons. Instead, click the 3 dots at the bottom, and click one of the RSVPs there. This will open the event in Google Calendar and send the RSVP from there and the sender WILL see that response. I did have one event recently that did NOT have those options under the 3 dots, and I have no idea why. Maybe a privacy setting of the event or something.
The other method I've found is to go to Calendar Settings>Event Settings and set the "Add invitations to my calendar" drop down to "From Everyone." Now when you get an invitation, it will appear on your calendar automatically (but only outlined to indicate you haven't responded yet) and then when you get the email you can go to your calendar and RSVP from the event itself instead.
Surprisingly, one thing I expected to work but did NOT work, was that I set up a new Google account using my domain address (so "me@mydomain.com" instead of a gmail address, which you can do now), and the main email RSVP buttons still didn't show my response for the sender, I'm guessing because the response is still coming from fastmail's servers and not Google's.
I do find this annoying, but usually those workarounds will get the job done. On the one where I didn't have second set of responses under the 3 dots that open in the calendar, I just had to reply to the sender to tell them I got it but they probably wouldn't see my response due to my non-gmail address.
Another thing I was surprised did NOT work: I clicked one of the main RSVP buttons so the event got added to my calendar (but again, that response did NOT show on the sender's end) and then I went to the event in my Google calendar itself and changed my response, but the sender still could not see my response. So once it's in the "broken" state, it doesn't appear as if there's any way to remedy it unfortunately.
Hope this might help someone in the future going through what I've been going through since I switched.