The “crazy cat lady” trope goes back generations. We all know what it means, and we all accept it. The “childless” adaptation was simply making his point.
This Purina “We are Cat People” commercial — the one I have embedded on this page on the right hand panel — uses the phrase (with “ crazy” — which you would think would be even more offensive than “childless”) repeatedly (go to 1:12 point). It’s targeted at people who have cats. And I’m sure a few of those people fit the profile Vance laid out. The video is still up after 12 years, so the company doesn’t seem to have received many complaints.