This is not a panacea because often people are not attuned to logical subtleties, but strife can be reduced by closer attention to distinctions. Even opposite assertions about what are actually different things do not conflict at all, except possibly through their implications. More qualified assertions also reduce the potential for conflict.
Claims of incommensurability tend to end dialogue rather than promote it, so it is not clear that they actually reduce conflict. Intelligible distinctions, on the other hand, are an important part of the implicit basis of civility. Much of civility and ethics is about appropriate response, which depends on intelligible distinctions.
Attention to distinctions is entirely consistent with a Kantian concern for ethical universality. It actually helps. We can do a better job of applying universals to particulars when we have more distinctions to work with. (See also Practical Judgment; Reasonableness; Contradiction.)