I came across this little article about some proper research being conducted about (American?) society's ace-phobia and possible psychological reasons for it. Just in case you need ammunition against the whole "asexuals aren't discriminated against like other queer groups are" nonsense.
Relatedly, the team of The Asexual Agenda and Asexual Muslim discussed a recent paper on the prevalence of mental and mood disorders among asexuals compared to straight people and other sexual minorities (homo- and bisexuals). The result in brief: Asexuals show significantly higher rates of depression and anxiety disorders than straight people, just like any other socially marginalised queer group. Who would have thunk.
- Scientific research on prejudice against Asexuals