It’s been over a year since I first posted that iCloud invitations to a non-iCloud (ex: Google) account have been broken since 2011. Briefly, if someone sends an invitation from iCloud to my gmail address I’ll never see it. Somehow Apple looks up one of the four (that I know of) iCloud accounts that I have, presumably one that references my gmail address, and uses that one instead.
In late 2016 Apple introduced an obscure workaround, an advanced iCloud (only) Calendar setting to receive event invitations by email — “if your primary calendar is not iCloud”.
I was working on a book chapter today so I revisited the old bug to check out the workaround. From my son’s (unused) iCloud Calendar I sent myself an invitation. Despite the setting nothing appeared in any of my (unused) Apple iCloud Calendars.
I waded through my Apple IDs to identify which one was associated with that Gmail address. I had to answer Apple’s “secret” questions  several times, but I found an Apple ID of mine associated with an iCloud account that did had the “receive by email” option enabled and had iCloud mail services. I tried from several iCloud accounts; none of the invitations appeared anywhere. They didn’t show as email, they didn’t show up on my iCloud calendar. They went into the ether.
Apple iCloud calendar invitations to non-iCloud addresses are still broken.
 Multiple iCloud accounts, some with email services and some without, is a longstanding Apple fiasco. Cook promised to clean it up several years ago and quietly abandoned hope. I periodically read hints from insiders that Apple’s identity management is more screwed up than even the most cynical outsiders can imagine.
 Also known as a hacker’s best friend.