@Per Lindblad, Thanks for posting in Q&A. From your description, we understand that you encounter Conditional access error 53003 when the device is compliant.
For the Conditional access error 53003, it means BlockedByConditionalAccess. Please check the user Sign-in logs which locate in Intune admin center > Devices > Conditional access > Sign-in logs and see which setting is blocked.
Here is a link about how to troubleshoot Conditional Access Policy problem:
Troubleshooting sign-in problems with Conditional Access - Microsoft Entra | Microsoft Learn
I notice the device is compliant in Intune. Please also check which compliant status of the affected device In Azure AD.
Hope above can be helpful!
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