When European countries want to pass unpopular legislation, instead of proposing it domestically, they propose it as an EU law, and turn back and say "look what EU made us do!". EU-wide successes of course are reported as personal achievements of whoever is on TV. Pro-EU vs anti-EU is also often a rallying topic in establishment vs opposition political debates, which tends to produce exaggerated controversies, sort of like the topic of abortion in the US. So I think there will always be some voices saying EU wants to outlaw curved bananas.

European countries are very different. I'm not sure if more than California vs Alabama. However, people remember that European countries used to have actual wars with each other throughout their history, up until not that long ago, so it's preferable to have disagreements worked out bureaucratically, even if that's a lot of bureaucracy.