Here's a clue: it definitely has to do with the network or ISP you are using to connect. I switched from my ISP to a tethered iPhone (not on WiFi) and the connection succeeded. Now, normally I would just think this was my ISP blocking the CDN -- however, a whole bunch of people on this thread all started reporting this issue at the same time. I'm not a network engineer, but my guess is that somehow some part of Apple's CDN network wound up on a blocklist somewhere, and some ISPs picked it up and others did not. Happy to be corrected if someone has further insight, but for those still experiencing the problem -- try switching to a different network and see if you can get past the loading failure.

Tried deleting and re-sending the invite, per @CalDevGames suggestion, and it still fails for me.

I'm seeing this issue, too (HTTP 401) when trying to click on the "Accept Invitation" link. I've filed a Feedback Assistant ticket #22586831 and have included HAR logs demonstrating the problem.