I think parent's point is that by searching for a double-crux you might obfuscate high-level generators of disagreement, so the conversation might progress but won't actually change anyone's mind even if there is a purely factual answer to the double-crus.

I think parent's point is made later in the paragraph after the section on double-cruxing:

> High-level generators of disagreement are what remains when everyone understands exactly what’s being argued, and agrees on what all the evidence says, but have vague and hard-to-define reasons for disagreeing anyway. In retrospect, these are probably why the disagreement arose in the first place, with a lot of the more specific points being downstream of them and kind of made-up justifications. These are almost impossible to resolve even in principle.

I.e., many people who have strong opinions on gun control would never agree to this sort of double-crux. And even if they did agree to it in the context of one conversation, and then "lost" the argument on that basis, they wouldn't actually go on to change their mind. They would return to the "High-level generator" and everyone just wasted their time.