Does the way you answer DEI questions change your odds?

That’s the only thing I can really think do call them is DEI questions. I really want to know as an applicant: does selecting “Choose not to identify” from any of the personal questions on an application screw your odds at all?

I have disabilities and always choose not to answer. It’s usually available as an option for that and veteran status (some places also have race, sexuality, gender, etc. that you can also opt out of). Does doing this mess up my odds?

I thought it was literally illegal for them to do that, but I guess who can really prove that was the reason they didn’t select you right? Maybe it all depends on the recruiter idk.