Why would people who don't want to have sex need to organise in any way?
I don't get this, either. Nobody ever got thumped in the street because they weren't holding someone's hand.
And in the wilder reaches of ace "discourse" that I've seen, there's often a thing about "dirty allosexuals" (allosexual = their word for people who aren't asexual), which since lesbians, gay men and bi people have been told gay sex is dirty for forever, pisses me off.
(And there's another thing where people who identify as asexual still choose to have sexual partners and say they experience desire, and so I am baffled as what the fuck asexuality is supposed to be anyway.)
I'm all for people having as little, or as much (safe, consensual) sex as they want. Actually being asexual = fine, and relatively common. Insisting it makes you queer = not fine.