There is no generic solution for that and randomly embedding HTML content you do not control will always yield unpredictable results. After all, what guarantee do you have that full screen ads are not the next annoyance that end up on your screen?
There is no simple way to reliably remove those cookie “popups”. There are filter lists within ad blockers (like for example fanboy-cookiemonster, 16000 rules!), but at the moment the browser doesn’t include an ad blocker extension. And all that is bound to break and unreliable.
You might be able to work around that using the scripting ability, but it’s not going to be fun.