The fact that the class structure has been complicated does not mean it has disappeared, nor does the increase in class mobility mean that classes have disappeared. It's worth noting that it's not only the 19th century theorists who thought of capitalism as class society, but relatively recent ones too. The notion that the "concrete aims" of Marx and company (if you're referring to them) have been fulfilled is farcical - they didn't only call for an increase in living conditions for non-capitalists, they called for a society different in kind, not just degree. I'd be interested in how core ideas such as "abolition of the value-form" play into a system to which they are antagonistic (market economy).

A lovely quote from the 60s:

“If the worker and his boss enjoy the same television program and visit the same resort places, if the typist is as attractively made up as the daughter of her employer, if the Negro owns a Cadillac, if they all read the same newspaper, then this assimilation indicates not the disappearance of classes, but the extent to which the needs and satisfactions that serve the preservation of the Establishment are shared by the underlying population.” (Herbert Marcuse)

And from the same person:

“Not every problem someone has with his girlfriend is necessarily due to the capitalist mode of production.”