Not competing with fish and shrimp means not caring about small interests or taking advantage of others. In the river, fish and shrimp belong to small ordinary creatures, just like people who do small business in society or small people who only look at immediate interests. Those people will only make people who do big things feel disgusted and helpless before interests, so not competing with fish and shrimp usually means not caring about small people.

Rotten fish and shrimp are not idioms, but proverbs. Rotten fish and rotten shrimp. Rotten fish and rotten shrimp literally refers to all moldy and spoiled meat dishes.