Exactly - it's very subjective. So how does a subjective emotional response give anyone the right to tell others how they may live?
I personally don't condone quite a number of things - killing and eating dolphins and whales among them. I also don't condone people carrying guns, spearfishing, eating lobster - lot's of things actually. I would never do any of those things myself - but I don't see that as giving me any right at all to tell others that they can't if it's legal where they are.
As abhorrent as the Taiji & Futo dolphin hunts are, they aren't illegal. For at least part of the Japanese whaling hunt, that is also permitted in clauses in the convention. Quite probably all of it is. People might wish it wasn't so and actually pretend that they're right and what the Japanese do IS illegal - but the fact is it isn't. If it was I'm quite sure the Australian CG/Navy for one would be arresting people and impounding boats as they do frequently in the case of other illegal fishing in the Southern Oceans.
People may not like it, but that's how it is. It doesn't matter how many times anyone says differently, and that even if it's not illegal it should be etc etc as it stands now the Japanese are operating within the rules of the IWC.