I think that relativism, by itself, does not have one particular set of ethical or political implications. Relativism as I understand it is not a stance or a position; it operates as a toolkit, a way of doing things. What it implies for ethics or for politics depends on what aims you direct it to.
If one aims to establish or perpetuate relations of domination, relativism can help with that, unfortunately.
But I also believe that if one aims to establish relations of equality, reciprocity, mutual accountability, and so on, relativism can help with that too.
My desire for a social movement that is inclusive of cultural and epistemological difference comes from my notion of socialism, not from relativism per se. Relativism only helps me articulate that desire and imagine its implications in particular ways that I that find fruitful.
Indeed, one can very well pursue the inclusion of cultural and epistemological difference using essentialist intellectual tools – along Habermasian lines, for example. Inevitably we encounter contradictions and problems by doing this. But then again, we encounter problems using relativist tools also.
I think we choose an intellectual framework as much for its problems as for its solutions. Which set of problems do you find more interesting, more fruitful to work on, more likely to take you in the directions you want to go?