SUPEE-9697 has broken the Design Exceptions functionality of Magento Enterprise with Full Page cache. This feature is normally used for serving a mobile theme.
To recreate the issue (with full page cache enabled and a design exception defined):
- Flush full page cache.
- In Chrome, enable developer tools and toggle the device toolbar.
- Switch to a device which will activate your theme (e.g. an iPhone).
- Visit the site and confirm you see your mobile theme.
- Toggle the developer tools device toolbar so you now see a desktop view.
- Refresh the page.
- You will see that the template being served (by full page cache) is the mobile template, which is incorrect.