"There is a rather enormous difference between things I care whether lwers do and things I care whether lw does."

This actually makes a fair amount of sense to me. There's a few ways to interpret it. The most obvious one to me is "Less Wrong has a reputation, built into its mission statement, about caring about rationality, winning at life, etc. I value those things." Depending on how collectivist you are, you might either care that people can look at you, say "That person is a LWer," and then correctly infer that you care about rationality and winning at life.

Or, more collectivist-y (which ordinarily I'd give higher likelihood to but maybe not in this case), one might enjoy feeling an identity as a Less Wronger, which includes, built into that identity, caring about epistemic truth and instrumental victory.

I can definitely see it unpleasant if "being a Less Wronger" came to be known, both among the community's allies and enemies, as (insert arbitrary thing you don't like here)

For example, I'm not a Objectivist, but Less Wrong terminology shares some common ancestry with Objectivism. So when I'm explaining LW to new people (especially more liberal people), I often get "wait, so is this an Objectivism thing?" which is annoying to me, not just because they are drawing false conclusions about me which I have to correct - but also because I don't really like Objectivism and it leaves an icky (irrational) feeling just to feel connected to that movement.