Hi there! I'm on Catalina 10.15.3. This issue was before and after the upgrade to Catalina, and started when the iOS Reminders app updated. This killed Reminders on my iMac because it is too old to update (annoying, it's a freaking Reminders app), but my phone and iPad Mini 4 are properly syncing.
The Reminders on my Macbook Pro don't work at all. Nothing. I'm fully updated, I've added and removed the account associated with it, I've restarted obviously. Chat support couldn't figure it out… I am SO confused. It works on my iPad/iPhone/iCloud desktop website.
This is crazy to me, it's not like I'm updating complex software, it's literally a Reminders app. This is one of the dumbest things Apple has done, which is saying something. Most of my searches find tons of issues with iOS but nothing specifically like mine. See attached for what happens when I open Reminders.