In Larry Sitsky's Music of the Twentieth-Century: A Biocritical Sourcebook, Jonathan Kramer offers that Morton Feldman was a modernist, but may or may not have been an avant-gardist. By his definition, a modernist is producing "art for art's sake", with an emphasis on elitism. An avant-gardist on the other hand is trying to provoke the conventional music world, often in a brash and aggressive manner, and where reaching a larger audience helps the cause. In the case of Feldman, independent of any aspirations of a broader audience, his music may be the opposite of aggressive, which in turn might have been a way of challenging the status quo given the norms of late twentieth-century art music.
I am listening to the performance of Feldman's For John Cage by Paul Zukofsky and Marianne Schroeder. From an abstract of a paper, Catherine Costello Hirata (who also authored the Feldman entry in Sitsky's book) writes:
On the largest scale, Morton Feldman's For John Cage (1982) for violin and piano is shaped by the contrast between passages which adhere rather strictly to the form 'aa . . .bb . . . cc' -- where each letter stands for what I will term a musical figure (usually comprised of but a handful of notes)-and passages which exhibit looser or more elaborate constructions...
And by the way, John Cage is clearly a member of the avant-garde, but even he has music that transcends the avant-garde ghetto; for me, his percussion music, his prepared piano music, or his simple piano music.