I think public opinion polling might actually solve the problem, because the actual group has greater moral authority than language police activists. I suspect people might not cite this Atlantic article during a discussion of whether their organization should adopt language policing for fear of coming across as a reactionary old fogey. But if you were citing a poll of the group in question, that's a level of moral authority that's hard for a language police activist to argue against.
Basically the hypothesis to test here is that a latinx-type reaction is fairly common, it just doesn't generally reach public consciousness the way it did in the case of latinx.