Over here, you can see that Reminders is using a different date format from the one I have set in System Preferences.
How do I get it to conform to the date format I have established in System Preferences?
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The Reminders app doesn't respect custom date format. It adheres to the default format for the currently set region and ignores any further customization made to the date format.
Apple support document, macOS Sierra: Customize formats to display dates, times, and more, specifies how date, time, number and currency format can be changed which is then respected by certain apps like Finder and Notes.
The document doesn't mention any app other than Finder and Notes and makes an ambitious statement:
Your formats are visible in Finder windows and in some apps. For example, dates in Mail or Notes show your custom format.
It's likely a bug in Reminders app or this could be by design. If this functionality is critical for you, consider filing a bug report (RADAR) using Apple Bug Reporter.