There is no such thing as a unified European, Western or White culture. As there is no unified Eastern or Asian culture. I get what they meant - puritan protestant English culture, predominantly sexist, classist and racist. The kind of Europe that bred the modern US which is perceived as the "Western culture" today. But that's not European. It's industrial period English. There is also a point to make for Athenean culture (not Greek or Ancient Greek, as Athen was more or less it's on country back then, even if it had some influence over the rest of what's now Greek - similar to how protestant English and Dutch views shaped huge parts of middle and northern Europe and extremist-catholic views shaped the Southeast).
But then there is a French tradition, a German one, a Swedish, a Swiss, a Polish, an Italian, a Spanish etc. Europe is and will be a hodgepodge and that's surely one of the reasons why the EU as a political system is pretty useless (as of now, who knows how it will evolve). We all learned our diffrent lessons from history, from somewhat diffrent histories even. Have a look at the middle ages or the early modern times, look at how extremly diffrent we've progressed (especially England, Austria and France, a little bit later Germany).
And then look at how we in Europe almost collectivley scratch our head about the US. It's diffrent. In a lot of ways. And we're proudly diffrent from each other as well. That's why Europe is rife with racism, but in a diffrent form than rascism happening in the US. That's why some problems don't seem to concern us (as much). Because we have our own typical problems which we should take care of first. And my, we have A LOT of them, even if we exclude things like colonialism and the major World Wars from the list. Does America even know that there's a 3000-year history between diffrent European contries and their cultures?
Also: Disney stole European fairytales and made them into distinctive US-versions. The dwarfs had neither names nor personality, but the huntsman was a major character. Cinderella is an amalgamation of diffrent similar tales from middle and eastern Europe. And what the heck is this Rapunzel-story? (Don't get me wrong, I like Tangled a lot. But it's not the German tale anymore. And Frozen is an abomination of the original Andersen-story, as is The little Mermaid). The white US entertainment industry "steals" from all of us and makes it their own. So maybe we should come together instead of trying to hate on each other. This only empowers the wrong people.