I spent over an hour updating devices to get "Family" (shared) Reminders working again….and it still isn't. Then I find this, which is a bit infuriating:
…but these articles are from September. SURELY this is fixed by now….right?! All devices are on iOS 13. When I send the invite to my wife's phone we accept it but then…nothing. There was a yellow exclamation point on the "Family" reminders previously (which I erroneously assumed upgrading to iOS 13 would fix), but after the upgrade didn't fix it, I tried re-creating and re-sharing, but no luck so far.
Best Answer
My apologies to the AskDifferent community - this was mostly just a rant due to frustration. After updating my iPhone to iOS 13.3 (like the other devices) then resharing the "Family" reminders, they started syncing with my wife's phone. I was just being a bit impatient, then those click-bait articles put me over the edge. :/