The rendering mode in Internet Explorer 11 can appear stuck if the site is added to your local Compatibility View list. When this happens, the rendering mode inside the developer tools and out will default to the specified compatibility settings.
While this may not be the only way a site can get on this list, Microsoft does document the steps for how to manually add a site to this list.
From Fix site display problems with Compatibility View:
To add a site to the Compatibility View list
Open the desktop, and then tap or click the Internet Explorer icon on the taskbar.
Tap or click the Tools button, and then tap or click Compatibility View settings.
Under Add this website, enter the URL of the site you want to add to the list, and then tap or click Add.
Site Compatibility View Removal Instructions:
To remove a site from this list, follow these instructions.
- Go to Tools > Compatibility View settings.
- In the resulting dialog, click on the site you want to remove from the list.
- Click the Remove button.
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