I agree that it is unusually sloppy work to cite InfoWars. It is especially unusual given that the rest of the paper seems to me quite well-researched and well-reasoned.
That said, I think it is too strong to say, “The author suggests that we should essentially stop talking about microaggressions in the ‘real world’ until these recommendations are met.” I agree with Lillienfeld that aggression requires intent, whereas “microaggression” encompasses a range of unintentional faux-pas or inadvertent indications of stereotyping. To continue calling all these things “aggressions,” to distribute lists of them, and to sell training programs against them may be premature. Lillienfeld is quick to point out that none of this contradicts the seriousness of prejudice in society or the importance of interpersonal sensitivity and awareness.
All in all, I still must conclude, as you do, that “The scientific recommendations the piece makes for the microaggression field are both reasonable and rhetorically interesting.” I will be keenly interested to watch the social science of prejudice, stereotypes, belongingness, and unintentional slights study these issues and improve our ability to help the underprivileged.