There are a lot of opinions on this but is it important? The lazy side of me would like to avoid separating the shrimp from the cysts but I would hate to be wrong.
Possibly the reason to separate them is purely esthetic. It looks messy but if it doesn’t bother the fish, it doesn’t bother me.
Another reason to separate out the cysts I found on the internet was the baby fish could choke on the cysts. I thought the reason for using brine shrimp was fish fry only eat things that move. All the cysts I have seen don’t move. Well… at least mine don’t. The part about the fish fry only eating moving things may work for killies but live bearers and angel fish fry for instance, can be raised on dry food so they may try to eat the cysts. The conclusion I come to here is it depends on the fish species.
The part about the cysts fouling the water doesn’t seem to be a big factor. In fresh water, the cysts don’t seem to break down that fast, in fact they last quite a long time without any of the usual signs of fouling the water such as fungus or high nitrite or nitrate levels. Possibly it is the uneaten shrimp that are fouling the water but I always have a population of shrimp in the fry tanks which take care of any uneaten dead shrimp. Snails are also a good option after the eggs are hatched but not before they hatch.