It's a pretty standard criticism of Lyotard, with whom that description of post-modernism is perhaps most widely associated. The Stanford Encyclopedia of Philosophy - which is a quite well-regarded source - has a very readable account of Lyotard's intellectual background https://plato.stanford.edu/entries/lyotard/#InteBack which relates quite plainly that he was far from intellectually consistent in his rejection of metanarratives (or "narratives about narratives"). Rather, a number of contingent political shifts in his outlook on the French society of his time seem to have played a larger role in how he chose to frame his arguments.

Given how closely this description of post-modernism is associated with Lyotard, one can only surmise that other post-modern authors were, if anything, even less consistent with it.