Dialetheism is not the view that "there is no distinction between "right" and "wrong"". Dialetheism is the view that there is at least one true contradiction. That's all. Most dialetheists believe that contradictions are very rare, that they only emerge in very special kinds of circumstances. And note that even in those circumstances in which contradictions do arise, it's not that there's no distinction between right and wrong. Suppose we accept that the Liar paradox ("this sentence is false") is both true and false, a contradiction. In that case: it's wrong, simply incorrect, to assert that it's not a contradiction.
You might be thinking of trivialism, which is the view that everything is true (and conversely, obviously, everything is false). All trivialists are dialetheists, but not all dialetheists are trivialists. Trivialism would destroy any distinction between right and wrong. But is there anybody who seriously claims to accept trivialism? (I know of at least one author who has explicitly defended it. I'm apt to consider his work, and any work like it, a purely technical exercise.)
What is is like it o lump it.
When it comes to "true" or "false" the word concept has to be defined in an isolated manner. False means false not bad, wrong or incorrect. What is hidden beneath this concept of communication is the emotional content due to the responses each persons individual belief system allows.
When it comes to belief you cannot believe what you do not believe ... or can you? Is it not the language that creates our conceptual boundaries (as well as other things)?