Now imagine that one day, you're talking with someone who you strongly suspect is a Blue, and they remark on how irrational it is for so many people to believe the moon is made of cheese.

I'm a big fan of "Agree Denotationally But Object Connotationally" when this is the case

Or, when talking to your fellow Greens about the moon, you would "agree connotationally but object denotationally". I find that for me this is actually even more common than the reverse.

think of the "skeptic" groups that freely mock ufologists or psychics or whatever, but which are reluctant to say anything bad about religion, even though in truth the group is dominated by atheists.

Okay, let's run with that example. If someone says something like "Theist are stupid"...I agree denotatively in that I think theism is foolish and I'm aware that holding theistic beliefs is negatively correlated with intelligence. I disagree connotationally with the disdain and patronizing attitude which is implicit in the statement, and I dislike the motivations which the person probably had for making it. If the same person had said "religiosity is negatively correlated with intelligence", then I would have no objections -it's the exact same information but the tone indicates that they are simply stating a fact. For particularly charged topics, explicit disclaimers voiding the connotations which normally occur are helpful.

I'm not sure it's practical, as a reader, to read writing and extract purely the denotative information, simply because of the sheer volume of useful information which is embedded within the connotations. If language is about communicating mental states and inferring the mental states of others, you can't communicate nearly as effectively if you toss out connotation.

TL:DR for Yvain's post: "Your statement is technically true, but I disagree with the connotations. If you state them explicitly, I will explain why I think they are wrong"