That entertainment often misrepresents traits does not mean that it itself does not form part of those traits. E.g. nobody would suggest Monthy Python accurately reflects British culture, but Monthy Python is part of British culture, and in many ways shines a mirror to it that most people won't get unless they've lived here for a while. The more those things are shared and become a common heritage the more they come to form a shared culture.
Shared fairy tales is a good example.
> All of the countries on the west side share very similar views about worker rights, welfare state, public education and healthcare, women rights, minorities' rights, democracy, etc. etc.
All of which had to do with extensive organising across borders for many decades, often out of necessity due to extensive repression (e.g. Marx had to flee both Prussia and France). If that is the level of ties you talk of, then sure, but that is a far more complex process, and it took a couple of centuries for Europe to harmonise on those issues despite that extensive effort.
If anything this is a good example of my point of how slow this process is.
The other examples you give are examples of diffusion of culture over far longer (centuries to millennia) periods, so hardly makes the point.
> If we compare western Europe to former eastern block countries we will find fundamental differences and that's completely normal (and sometimes scary), because we have been separated for a long time and we are still compensating for that time.
Those differences did not come into being with World War II. They were pronounced for centuries before that.
The point is not that contact does not matter. Of course it does. It is that diffusion of culture takes a long time, but shared cultural heritage - including light entertainment is an important part of that, because you're never going to understand someone perfectly without sharing their cultural references, and they go all the way back to childhood.
All those things you mention matter, but spreading them are easier the more people understand the same terms and references, and laugh at the same things, and know the same stories, and have heard the same music.
Heck, you pointed to the EU, whose anthem was chosen in part because it is a piece of music that is near universally known, and as such provides a reference to a shared heritage.