As a relativist, I don’t see myself as an anti-realist, but as an irrealist.
To say “the world is not real” or “it is the case that all things are relative” makes a pretty obviously self-contradictory statement. I’d prefer to turn aside from this binary opposition of “real/not real” altogether.
I understand relativism as a movement, a gesture: that of taking something identified as fixed, essential, or universal, and treating it as fluid, relational, contingent. Taking things which appear, in our thoughts and actions (our praxis), as absolute, and relativizing them.
I find myself endlessly curious to see how far this gesture can go.