There are a few ways that applications can protect the files that they create. Ownership and permissions are an obvious and transparent mechanism, but that protection has limitations. For even more protection of the most privacy-sensitive data, macOS defines a handful of "data protection classes". Two of those data protection classes indicate that a file can't be opened unless you're logged in and the screen is unlocked. Any application can bestow this protection upon files that they create. For example, some Apple applications (like Mail) use this protection class to protect files that store recent search history, and WhatsApp applies this protection to downloaded image files.
How does this affect your backup tasks?
If a backup task runs when you're not logged in, CCC won't be able to open the files that have this special protection. By default, CCC doesn't treat these incidents as errors, rather it simply tries again to back up those files when the backup task next runs. The condition is often transient, and based on a lot of feedback, most users found the errors to be a nuisance when we briefly set "report as errors" as the default behavior during beta testing.
There is no "one size fits all" solution for this condition. What's right for your backup really depends on what sorts of files have this protection on your startup disk, whether your backups tend to run when the screen is locked, how aggressive you want to be in getting these files onto your backup, and whether you even want to have these files in your backups at all.
To help you make the best decision for your own backups, CCC pulls together as much context about the files as possible. CCC retains a list of affected files and will present a notice in the Backup Coach (look for the 
icon in the Task Plan) where you'll be able to see the list of affected files. You can also see a list of affected files for all tasks (if any are present) in the Advanced pane of CCC's Settings window. If Apple Intelligence is available and enabled on your Mac, CCC will use on-device Apple Intelligence to offer some additional context about the content and purpose of each file, based on the file's name and location.
Customizing the handling of these files when they can't be opened
CCC offers a couple options that allow you to see the affected files and to apply granular control over their handling. Click Settings in CCC's toolbar, then select the Advanced pane in the Settings window sidebar to find these options. If any files are in a deferred position, click the Show suppressed items… button to see a lit of the affected files.
Report the affected files as errors
When CCC is unable to open a file protected by a Data Protection class and this setting is enabled, the task will conclude with an error. Each affected file will be listed in the Errors tab of CCC's Task History window. When an affected item is selected, you can click the "Ignore this error for this file" button to suppress future errors affecting that file (but the file will still be backed up whenever the task runs while you're logged in). Click the "Exclude From Backup" button if you don't want to include the file in your backups.
Repeat affected tasks on login
When this setting is enabled, CCC will automatically repeat an affected task when you log in to your Mac or unlock the screen. The affected files will be backed up, thus immediately resolving the transient condition.
Retaining the confidentiality of information in these files
The data protection that's applied to these files is unique to an Apple Silicon Mac's startup disk; that protection doesn't carry over to a backup disk. If you want to retain the confidentiality of these files, be sure to enable encryption on your destination volume. To enable encryption on your backup volume, click Volumes in CCC's sidebar, then select your backup volume in the sidebar and toggle on the FileVault switch.