Reminders from iOS 13 / macOS 10.15 Reminders aren't syncing
When you launch Reminders the first time on iOS 13 or macOS 10.15, it asks you if you'd like to *Upgrade* your reminders. If you choose _Yes_, then these calendars will no longer sync over CalDAV and thus will not work with third party apps.
Upgrading Reminders presumably adds support for additional features that renders it incompatible with third party apps syncing over CalDAV. This affects all third party apps, including BusyCal, that rely on CalDAV to function.
Shared calendars in particular will cease to work. Your best bet may be to create a new calendar in BusyCal, and setup sharing from within BusyCal again. This should continue to work across iOS 13 / macOS 10.15 provided you do not "Upgrade" these calendars when prompted by Reminders.
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