We need a pluralistic– a pluralism that also recognizes different animal worlds as phenomenologically described by Uexkull –to cultivate compassion and proper ethical regard for others; a big part of which involves recognizing the limitations of ones own conceptual schemes, attempting to understand others, or at least recognize that they might inhabit worlds of meaning (in Heidegger’s sense) that differ substantially from our own. However, we need a realism because there are facts of the matter pertaining to what causes psychic maladies, climate change, how economy functions, etc., and when we get these things wrong we generate horrific practices. How, then, can these things be thought together? I don’t know. It seems I’m continuously trying to square circles.(Well, let me try to circle that square! ... sorry.)
Ontologically and metaphysically the idea of realist pluralism is no longer an issue. There are (appropriately) numerous variants but the basic idea that reality is itself pluralistic is well established. The question is political-discursive. It's what Stengers and Latour are getting at with their concepts of diplomacy and cosmopolitics.
They grant, first, that all entities exist and, second, that to say that someone's cherished idol (or whatever disputed entity they hold dear) is non-existent is a 'declaration of war' - 'this means war,' as Stengers often says. They thus shunt onto-political discourse off of the terrain of knowledge/belief in the sense of existence/non-existence. Their basic claim seems to be that 'respect for otherness,' i.e. political pluralism, can only come from granting the entities that others hold dear an ontology, even if you don't 'believe' in them. You are thus permitted to say 'I do not follow that god, he has no hold over me' but you are not permitted to say 'your god is an inane, infantile, non-existent fantasy, grow up.' And it's not just a question of politeness (although there's that too). The point is to grant others' idols and deities an existence - one needn't agree over what that existence entails, over what capacities that entity has or what obligations it impresses upon you as someone in its partial presence but to deny it existence entirely is to 'declare war' - to deny the possibility of civil discourse, of pluralistic co-existence.
I think it's important to add that they do not deny the possibility of legitimate 'war talk' - perhaps there are circumstances where that is entirely justified, in fact it's inevitable - but the properly political question should be 'how can we live together?' That is not a utopian political programme but a pragmatic one. And that's also the root of the notion of the composition of a common world through diplomacy.
I found (and still find) this a difficult notion to get my head around. The notion of 'speaking your mind,' of 'saying what you really mean' is so engrained in many ways that to temper that seems dishonest. But we do it all the time, in practice. That's 'political correctness' (which, contrary to reputation, has not actually 'gone mad').
Interestingly, although Stengers and Latour base this political philosophy upon their interpretation of anthropological praxis (combined with that of diplomacy), this kind of mutually accepting ontology is not entirely de rigeur within anthropology. Mario Blaser is developing basically the same set of ideas within anthropology itself, talking about ontological conflicts and political ontology.