Sure, that makes sense in the short term. But if everyone did this, over a long period of time, two things would happen:
(a) Diversity programs would at some point stop being ineffective.
and
(b) Identity politics would achieve cultural hegemony.
I agree that it would be wise to shut up if doing so had no long term effects (as in your example of a manager asking about religion), but that clearly isn't the case here. And in the case of (b), I would say that long-term effect is extremely undesirable, for both businesses and individuals.
(a) Diversity programs would at some point stop being ineffective.
and
(b) Identity politics would achieve cultural hegemony.
I agree that it would be wise to shut up if doing so had no long term effects (as in your example of a manager asking about religion), but that clearly isn't the case here. And in the case of (b), I would say that long-term effect is extremely undesirable, for both businesses and individuals.