Given that the author used to work as an editor for the largest American dictionary publisher, it's more likely that the phrasing is deliberate and accurate. Assuming that, we can then figure out its structure and how it is grammatical.
"Our" is a possessive pronoun, so what follows must be something that can be possessed, i.e. a noun of some kind. Consider this similar structure:
In spite of their old-fashioned opinions, they can be open to new ideas.
They possess the opinions, so we use the possessive pronoun "their". Outside of certain dialects, we would not say, "In spite of they opinions". That's not grammatical.
"Being liberal commie descriptivists" is a gerund phrase that acts like a noun, and again, something that can be possessed by us. Expanding on the previous example:
In spite of their having old-fashioned opinions, they can be open to new ideas.
Possessive + gerund phrase. It's the same with "our":
In spite of our having old-fashioned opinions, we can be open to new ideas.
Grammar-wise using "us" changes "being" from a gerund to a verb, but there's little difference in meaning. The difference is in the style, and also in the nuance. The sentence clearly refers to some earlier comment where someone called them "liberal commie descriptivists" (for insisting "irregardless" is not a word), and suggests something like:
in spite of (us possessing the quality they said we have) ...
just with fewer words. In the right context, this use of the possessive pronoun can sound a little more sophisticated.