If you are trying to log into a service protected by Duo on your iOS device's web browser & are seeing a gray box (like the picture below) instead of the screen that lets you choose how to authenticate via Duo, this is most likely due to Content Restrictions being enabled.
There are 2 options to resolve the issue:
• To disable content restrictions on iOS 12, open Settings --> Screen Time --> Content & Privacy Restrictions --> Content Restrictions --> Web Content & click to uncheck 'Limit Adult Content'
• To disable content restrictions on iOS 11 (or older), open Settings --> General --> Restrictions --> Websites & click to uncheck 'Limit Adult Content'
• If you do not wish to disable content restrictions for all iOS versions, add duosecurity.com (do not add a www. in front of the website address) to the Whitelist - Always Allow Section by clicking 'Add a Website...' below the Allowed Websites section where Limit Adult Content is checked. See the screen shots below for more details
Always Allow Section Showing where to touch to Add the Web Address
Add a Website Screen Showing Exactly How to Type the Web Address
Click here to view the Duo webpage on resolving this issue.