I think the act of bringing postmodern tools to the debate was a way of playing the "I win" game by turning the conversation into inescapable morass for those that weren't accustomed to that kind of debate.
Whatever the "reactionaries" did in response was yet another step in the evolution of the back-and-forth and no more or less in bad faith than the previous step.
Yeah, there is a subtle distinction between “there are no neutral points of view” and “there is no such thing as objective truth”. Postmodernist arguments applied to contemporary politics serve to blur that distinction, which is where the bad faith comes in.
Whatever the "reactionaries" did in response was yet another step in the evolution of the back-and-forth and no more or less in bad faith than the previous step.