The instrumental view of elite culture views it, simply, as class privilege. People who have been the right schools, with the right cultural references, etc... will have access to the upper echelons of society, etc...
By definition elite culture belongs to the elite. Knowing literary references makes one more cultured and polisished. Those who don't have it, by the same token, are marked as less than elite.
Elite culture, in the second definition, is a resistance to conventional attitudes. It is not identified with any particular class position, and is in fact opposed to conventional "bourgeois" attitudes. Elite culture is the last bastion against the dumbing down of everything. A dumbing down that will serve corporate interests.
Take the example of Samuel Beckett. His prototypical protagonists are tramps or institutionalized homeless people. So we can take the example of an elite ivy-league graduate who knows who Samuel Beckett is, condescending to the community college graduate who doesn't.
But the experience that Beckett is describing is one of absolute social abjection, not social privilege.
It is easy to see that there are periods in which social privilege corresponds, unproblematically, to access to cultural capital. This does not apply, anymore, to modernist literature. Or it does, but unevenly. The divorce between a certain "class" position and the access to cultural capital might become complete at a certain point. We still see Virginia and Marcel as both upper class and culturally privileged at the same time; but not James Joyce, D.H. Lawrence, or Beckett.
Most leftist literary intellectuals are going to be invested both in a non-elitist politics, and in an interest in high-brow literary modernism as well. We know what the standard positions will be, already. The easiest cases are going to be those of marginalized but avant-garde subjects. Canonical writers of the avant-garge who come from socially marginal position, like César Vallejo. Just about everyone I most respect who knows anything at all about Latin American poetry thinks that Vallejo is the greatest Latin American poet. I think so too, obviously.