If it's bad enough and persistent enough it can irritate their gills. However in the wild streams get muddy once in a while and as long as it's not an on going thing the trout are O.K.

I had this problem when I first put my pond in. My contractor was supposed to put the pond in in early spring but didn't show up until September. Anyway not enough time to get grass established well, and even with straw I had a gully washer and chocolate brown water that stayed that way for a few weeks. Some of my brook trout had gill covers permanently fused in the open position due to infection.

If pigs could fly bacon would be harder to come by and there would be a lot of damaged trees.