I see no problem with stocking a somewhat muddy pond. Mine gets that way due to the occasional rains after our extended drought. The problem I find involves recruitment. Without sunlight penetration, you just can't get the bloom which fry need. No fertility always means poor recruitment. Eggs need sunlight penetration and oxygen. Suspended mud retards the growth of the planktonic base that is the bottom or base of the food chain.
It can be done but is a pretty poor second choice compared to a balanced pond. I've caught some really good, healthy bass out of a particular muddy lake that I love. However, I rarely caught a small one or one below about 14 inches. I also never saw a bluegill nor a small catfish. On a new pond, I would do it. However, I would artificially feed until it cleared.

It's not about the fish. It's about the pond. Take care of the pond and the fish will be fine. PB subscriber since before it was in color.

Without a sense of urgency, Nothing ever gets done.

Boy, if I say "sic em", you'd better look for something to bite. Sam Shelley Rancher and Farmer Muleshoe Texas 1892-1985 RIP Grandpa