However there are a lot of beliefs that make this kind of approach unworkable.
If XYZ wants to believe that the earth is flat, sure, that can just be a personal belief and won't interfere with his work duties... well, unless he is launching satellites for NASA.
If XYZ is a furry and thinks anime girls in cat outfits are hot, sure, that's cool too. Also a personal belief that probably won't interfere with work.
If XYZ is an anti-vaxxer... well, probably won't interfere with their job unless they work in medicine. A dumb personal belief but this can probably stay personal.
But suppose employee XYZ runs a newsletter (in his own time) and publishes views about how Jews or women or black people or whatever are inferior. Can you really trust this employee to do his job at your company, where he might have to interact with people from those groups?
So, I don't think a naive approach of "just keep work and personal beliefs separate" covers 100% of situations.
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.)
However there are a lot of beliefs that make this kind of approach unworkable.
If XYZ wants to believe that the earth is flat, sure, that can just be a personal belief and won't interfere with his work duties... well, unless he is launching satellites for NASA.
If XYZ is a furry and thinks anime girls in cat outfits are hot, sure, that's cool too. Also a personal belief that probably won't interfere with work.
If XYZ is an anti-vaxxer... well, probably won't interfere with their job unless they work in medicine. A dumb personal belief but this can probably stay personal.
But suppose employee XYZ runs a newsletter (in his own time) and publishes views about how Jews or women or black people or whatever are inferior. Can you really trust this employee to do his job at your company, where he might have to interact with people from those groups?
So, I don't think a naive approach of "just keep work and personal beliefs separate" covers 100% of situations.