Apple requires third-party apps (like Calendars) to use app-specific passwords with iCloud accounts. An app-specific password is a single-use password you generate on the Apple ID webpage and paste into the password field while adding your account to Calendars.
To generate an app-specific password, make sure you have two-factor authentication enabled.
Note: Some Apple IDs created in iOS 10.3 or macOS 10.12.4 and later versions are protected with two-factor authentication by default.
Please make sure that while adding your account to Calendars, you use your iCloud email address, not an iCloud alias. You can check your email address in Mail on iCloud.com (click on the Settings icon at the bottom right > Preferences > Accounts).
Note: App-specific passwords work only for the iCloud email address with the @icloud.com, @me.com, or @mac.com domain name. This address can differ from your Apple ID email address (e.g., your Apple ID may be linked to Gmail, Outlook, or other emails). You can see the iCloud email address you need in the “Reachable At”/“Contactable At” section on the Apple ID webpage.
If using the app-specific password didn't help, please check the following:
If the steps above didn't help, you can try connecting your account through local calendars:
Note: If you already have some of the accounts added to Calendars by Readdle and don’t want them to be added twice to the app, disable them in the Local Calendars section of Settings (⌘,). Disabled accounts will still be available for other apps and systems.