If i get you correctly, you are asking if fish as a source of protein should be abandoned if we discover that they are fished from polluted zones? I think the answer to the question is not as straight forward as some may think.

But the simplest answer to this question is that as far as there are still sufficient catches from the wild and the fish populations are still thriving and surviving exploitation, then the pollutants may not be significantly accumulated as to cause harm to humans on the short or medium term of a human life span.

The answer to this question is not as direct as some may think. But from a logical line of thought, if the fish populations are still thriving and surviving current exploitation rates, then the toxicants may not be significantly accumulated as to affect humans negatively on the short or medium term life span.

Acute problem of marine pollution is a reality especially in the developed world & many countries are now monitoring heavy metals presence on a weekly basis & advising their citizens about their quantum & how much of each of the commercial variety that can be consumed by an adult.Such a practice is still not carried out in the developing world.It is also a fact that fishes in the higher trophic level will have higher concentrations of these elements & compounds.So it would be safer to avoid these in the first instance & concentrate those in the lower trophic levels.Half of a fish population generally gets consumed by various predators in their natural systems,leaving quite a huge mass for others-say human capture.Pollution takes a heavy toll especially during the spawning & larval stages.Fish mortality declines as they grow older due to pollution,this is because older the fish,it can still escape accidental presence of pollutants to a certain extent.Fish is the cheapest source of animal protein,is high in Omega Fatty acids & can also be aqua cultured on a massive scale,whether on land,inshore or off shore.Aquaculture does away with the problems encountered in your question & for this reason it is very fast catching up with capture fisheries.

Fish is very nutritious food. It can also accumulate certain pollutants and represent more or less important (depending on amount and frequency consumed) source of exposure. Still other food from the meat group can also be an important source of exposure to the same pollutants and this should not be overlooked. Internationaly i think there is a ban on use or even import of fish (just like for other food) from certain heavily contaminated areas. 

Fish provides high quality protein. Fish, especially those at the top end of the food chain is also vulnerable to accumulation e.g. heavy metals and this can provide a health risk to people. Great emphasis should be given to decline marine, lake and river pollution. This is often a huge challenge in developing countries, where often industrial waste untreated are released to water bodies. In many developed countries in the 1970s water treatment has become an obligation and through this the challenge has been reduced.

Another aspect is that for long fish has been a cheap source for high quality protein. This was crucial especially for poorer sections of societies. Today fish has become one of the most expensive proteins, which has severe nutritonal consequences of poor population sections in developing contries

One of my studies found an increase in depression among those eating certain types of fish: Article Effect of 8-week program on individuals exposed to fish envi...

The world is suffering a food crisis because of the lack or lack of agriculture in most countries of the world and therefore the decline in the proportion of agricultural products such as vegetables and fruits, etc. Fish are considered the best solution to solve this crisis, but the production of fish at present is suffering from a decrease in the proportion of nutrients where - The proportion of nutrients and vitamins in fish has decreased significantly in recent years because of the low proportion of fatty acids in fish that protect against heart disease. The study, carried out by a team of researchers in Denmark and published by the Bursen newspaper, said the reason was that fish farmers marketed had stopped using fish-rich food and fish food was concentrated on vegetables and proteins that did not contain fatty acids rich in vitamins. Most of the fish that are marketed come from fish ponds and the food industry depends on the world markets, and very few fish come directly from fishermen who sell fish, which is fish, which is rich in acids. The fish also suffer from food crisis. Health and nutrition. According to a researcher at the University of Copenhagen, the reason for the reliance on vegetables to feed fish in fish ponds is due to the rise in the price of food based on fish oil. But the important question remains whether the name is safe and not contaminated with chemicals thrown into the water