Are Vegan-Only Job Adverts Discriminatory?

IANAL. The answer is "yes", and this writer is ill-informed on the topic.

In most US states you a free to discriminate for any reason except for certain protected groups. Eg, in many states you are free to discriminate on the basis of political party membership. See https://www.nolo.com/legal-encyclopedia/can-employers-discri... .

So, absolutely you may require vegan-only employees. (Check local laws for exceptions.)

Furthermore, this is specifically a job advertisement for the group Save Animals From Exploitation. They would very likely have a bona fide occupational qualification to discriminate. See https://en.wikipedia.org/wiki/Bona_fide_occupational_qualifi...

The author didn't mention either of these important and relevant points.

Sure.. but not illegally so. I mean a job advert for a programmer would discriminate against people who couldn't, or don't believe in the practices of the company.