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There seems to be a conflict between the EU-directive plugin and the Builder used in the Yootheme Pro framework.
If you're not familiar with this templating framework (it's a paid component), it's a little hard to explain what the problem is but my hint is this:
In the backend, when you edit the template, instead of having just settings to adjust, you have an iframe of the front end and you can use a "Builder" to "build" the page, adding blocks of elements (blocks of HTML, images, slideshow, J! modules, ...).
When the EU plugin is enabled, this does not work: the builder sys that the page is not connected to the theme, and so it can't be edited. There are no JS error reported by the console, but there is the message : The EU e-Privacy Directive extension REQUIRES the eprivacy module to be published.
So my guess is that the problem comes from that the EU plugin is not meant to work on the admin side, which is normal, but then it creates a conflict when you have the kind of Yootheme system.
I'm not sure you can do something about it, but I thought to report it. My workaround so far has been to disable the EU plugin while I'm editing something with the builder and re-enable it when I'm done. A little cumbersome but it's working.