It occurred to me that I could go straight to the source to answer the question. But after reading through this, it became apparent that this would be pointless, since Andrew Eldritch seems to have no idea about what he is talking about when it comes to postmodernism.
I can, off the top of my head, list several "postmodernists" who cared deeply about politics, to the extent of actually taking action. In philosophy, to name two names, there is Foucault and Deleuze. Both were classed postmodern (against their will, which seems to be the case with all postmodernists, as it is with certain people and the Goth label ), and both were ardent activists within Palestine liberation, gay rights and prison reform. In addition, Foucault seems to share Eldritch's respect for Anarcho-Syndicalism.As you may have gathered, the Sisters are a political animal. And caring about anything is so uncool. Too bad.
Now postmodernism seems to me to be a pejorative categorization for (A) modernists who are far too critical of the Enlightenment for the likes of Sokal and Dawkins, (B) modernists who treat fragmentation and discontinuity positively rather than negatively, and (C) modernists who don't see fragmentation and discontinuity as something which can be transcended. An example is William S. Burroughs: in his notion of the habit and the fix is presented the impossibility of transcending irrational, economically imbued desires, and in his cut-up technique is found the affirmation of fragmentation and discontinuity. Of course, all three do not have to be internalized by an artist to be classified postmodern (you only need to pass A and be slightly sceptical to be classified postmodern by Sokal); after all, this makes it a lot easier to pigeonhole people.
Andrew Eldritch seems to be dismissing a wide range of thinkers (although he may simply be using the dichotomy to highlight several of his dislikes, such as prioritizing muesli over human rights), but in doing so, he's doing what he loathes (perhaps jokingly). If I wished, I could easily stretch statements (the sisters are a band for a hard world, but a hard world you can get off on) until they extend over the barrier and land in the realm of affirmation of diffÃ©rence. But I shall leave that up to you after asking you this: are the Sisters modern or postmodern?