Not a cross racer or anything of the sort, but: I have M540s on my roadie, and the one time I had to walk the bike through dirt*, I had a heck of a time clipping back in or out until I stopped and dug the gunk out of the cleat with a stick. That didn't help much--I had to hose my shoes down.

*It wasn't so much dirt as a wet mixture of clay, sand and bits of rock. I think the composition didn't help anything--I'm pretty sure it's one step shy of cement!