You mean the collapse of Communism and 'the end of history'. They claimed that they wanted to overthrow capitalism but ended up trying to copy it. So now the old ruling classes have slipped effortlessly into the role of rulers in 'free-market' societies. There have never been genuinely 'classless' societies - one good reason, you might think, why there never will be. Equality would not mean we'd become identical.
Education is the crucial issue here.
Free education of equal quality for all is fundamental to a classless society. Education in class-based societies is wasteful of talent and teaches most children to devalue themselves so that they will fit in. It's hard to imagine anything more pernicious than this. Since many millions of people have no job at all, free-market economics hardly provide a perfect motive. In any case, we need to rethink the nature of work for the next century, because there will be less of it around.