The phrase "haddest bearing on" implies significance or relevance to a particular topic. Therefore, antonyms for this phrase could include "irrelevant," "inconsequential," "unrelated," or "trivial." Using these antonyms, one can convey that a particular issue is not important or relevant to the discussion at hand. Additionally, words such as "unimportant," "trivial," or "insignificant" may also serve as antonyms to the phrase, emphasizing that the topic in question is not crucial in any way to the given context. Overall, using antonyms of "haddest bearing on" can help to downplay or dismiss the importance of a particular point or idea.