If, after realizing an old mistake, you find a way to say "but I was at least sort of right, under my new set of beliefs," then you are selecting your beliefs badly. Don't identify as a person who iwas right, or as one who is right; identify as a person who will be right. Discovering a mistake has to be a victory, not a setback. Until you get to this point, there is no point in trying to engage in normal rational debate; instead, engage them on their own grounds until they reach that basic level of rationality.

For people having an otherwise rational debate, they need to at this point drop the Green and Blue labels (any rationalist should be happy to do so, since they're just a shorthand for the full belief system) and start specifying their actual beliefs. The fact that one identifies as a Green or a Blue is a red flag of glaring irrationality, confirmed if they refuse to drop the label to talk about individual beliefs, in which case do the above. Sticking with the labels is a way to make your beliefs feel stronger, via something like a halo effect where every good thing about Green or Greens gets attributed to every one of your beliefs.