According to the quotation from their web pages, main basis of their allegation seems to include the two main reasons below.

MUJI Views

1. MUJI is sourcing over 70% of its fins landed and processed at Kesennuma Port, Miyagi Prefecture, Japan and the rest of it from Spain. At Kesennuma, the Blue Shark is mostly caught by the long-line for tuna, yet, unlike so-called "Finning" prevailing in wide area getting only shark fins and throwing the rest of the body away back to the sea, whole body is landed at the port and wholly utilized i.e.; meat for various types of processed fish paste food, cartilage for health supplements, skins for the materials of arts and crafts.To make sure the facts written above, MUJI has delegated its staffs to Kesennuma to investigate the whole process by inspecting from the landing to the processing at plants.
As mentioned above, our way of sourcing fins is definitely different from what is called "Finning", or just killing sharks to get the fins only and throwing away the other bodies to the sea and it should not be equated with "Finning".
With regard to our souring from Spain, our suppliers are operating in accordance with the rules and regulations set forth by the local authorities, which is proved by the adherence certificates issued.In spite of above, MUJI intends to wholly shift our materials to Japanese Kesennuma origin at the earliest convenience aiming to improve the transparency and traceability of our materials procurement.

2. According to IUCN, quoted in their campaign, they have the Red List classification as below:

With regard to the classification "Ｎear Threatened", MUJI wishes to point out that this belongs to "Lower Risk" category and Blue Shark is ranked as the lower species in the class. Also, MUJI has investigated and confirmed that at this stage no regulations nor restrictions on the Blue Shark catching couldn't be found not only in Japan but globally though there are some rules and regulations prohibiting Finning.

From the situations written as above, MUJI has come to the conclusion that we continue the sales of "Shark's Fin Soup for Rice" for the time being.

MUJI has been working to introduce our world customers the reasonable and suitable products. And if it is allowed to add some words, MUJI "Shark's Fin Soup for Rice" is manufactured using the materials mainly from Kesennuma, Miyagi-Pref., where such processing has a long history as a local industry and our decision is also encouraged by our desire to offer small helping hand to the local people suffered from the tragedy.