To meet the rapidly rising market demand for fish and seafood, suppliers are growing fish twice as fast as
their natural growth rate, cutting their feed allotment by nearly half and raising them on special diets.
Meaning clarity -
We can say, "John walks twice as fast as Sam walks" - we are comparing actions.
Likewise, the sentence's meaning is "Suppliers are growing fish twice as fast as they grow naturally." They here refer to "fish." We are comparing how suppliers are growing fish with how Fish grow naturally. How are suppliers achieving it?
By two adverbial modifiers
1. cutting their feed allotment... (their logically goes to fish)
2. raising them on special diets...(them logically goes to fish)
Now, with this understanding -
(A) their natural growth rate, cutting their feed allotment - As Krishna also pointed out, the below two sentences using ellipses don't make sense
1. Suppliers are growing the fish twice as fast as "suppliers are growing" their natural growth rate. or
2. Suppliers are growing the fish twice as fast as their natural growth rate "are growing fish."
So a logical deduction is - Suppliers are growing fish twice as fast as they grow naturally." They here refer to "fish." We are comparing how suppliers are growing fish with how Fish grow naturally.
(B) their natural growth rate, their feed allotment cut - This one has not only a problem as described in A but also an additional problem of wrong modifier structure. "And" demands an adverbial modifier parallel to "raising them on special diets."
(C) growing them naturally, cutting their feed allotment - Who is growing them? Supplier? No. It says naturally. So how can suppliers grow then when they grow naturally? Moreover, here, on one side of the comparison, twice as fast as we have a clause, and on the other side, we have an ING verbal. Not parallel. Wrong.
(D) they grow naturally, cutting their feed allotment - perfect.
(E) they grow naturally, with their feed allotment - while the first part is correct. The modifier is not correct. "And" demands an adverbial modifier parallel to "raising them on special diets."