The interesting thing is that the hypothetical "publishes views about how X are inferior" is considered OK if "X" is "male" or "white", say.

I understand the arguments from a structural racism/sexism standpoint for treating those situations differently from the ones you describe, but the specific test you propose seems to fail just as much: can you trust someone who thinks men are inferior in a job where they might have to interact with men?

(I will note that your use of the male pronoun in describing the untrustworthy employee is itself interesting; not sure whether that's meant to be a gender-neutral "he" or whether you actually believe that only males can hold "undesirable" views.)