It's fun to read the extent to which Schelling goes up against it. His reason? Modern concepts (post-Hume, post-Kant) are very valuable, but there is a lack of intermediary concepts that can allow us to think, for instance, how a body can start to think, how humans acquire a psyche (this is not strictly his argument, but it's quite relevant), and so on. If you really want to be a materialist, it might be a good idea not to cleave so tightly to LNC.
One of the more distressing things about Martin Hägglund's "radical atheism" is the extent to which he relies on LNC, in the name of Derrida (what's wrong with that phrase?!).
I'm trying to get Graham Priest over here to do a talk fairly soon. Priest is, if you don't know, the maitre d' of contradiction.