People acting in bad faith will misinterpret even well-specified statements if they think it will benefit their stance - we shouldn't assume that being more specific in our language will allow us to win debates against people who have already decided that their own opinions are correct, and won't listen to anyone saying otherwise. Those discussions will always devolve into the nonsensical associations you described. Instead, we need to be as specific as possible about what we know, while simultaneously leaving our statements open when there is information left to be gathered and added in, and we need to teach those who interact with us in good faith that that is the reason for leaving things unspecified.

To use your example, we have red cups and blue cups. Nobody knows anything about them, but then my friends and I all grab several blue cups and find that they're all hot. We say "careful, the blue cups are hot" not because anyone should assume the red cups aren't, but because we don't currently know anything about the red cups. You can infer that the red cups are hot because they're alongside the hot blue cups, or you can infer that the red cups aren't hot because they're a different color, both of which would be informed, potentially correct assumptions, but until someone touches a red cup, nobody knows one way or another. That is the point of using a combination of specificity and ambiguity - it allows people to quickly understand what you know, as well as what you don't currently know, and allows space for new information to be added as we work together to figure out the truth of the situation.

Bad actors will misinterpret statements regardless of their specificity, but our behavior is not focused on them; our behavior is intended to work well together with the good actors. Tailoring your statements to address people who have decided to be antagonistic doesn't work, because people will always find ways to be antagonistic. Instead, tailor your statements so that people who have decided to listen with the intent to work together to come to an understanding will be able to do so most effectively.