It may be relevant that asexuals started coming out after homosexuals did.

I don't think asexuals were really in the closet until relatively recently. After all, many denominations of Christianity provide people with reasonably high status positions that require that the person abstain from sex. Even the denominations that don't have monastic traditions wouldn't look down on someone who abstains from sex. It wasn't until the sexual liberation movement promulgated the idea that anyone who isn't interested enough in sex is a prude and probably repressed that asexuality became something unacceptable.