They claim it has no bearing on the hiring process. Is this true, generally speaking? Or does selecting prefer not to disclose give a bad first impression?
Company is a tech company, less than 500 employees.
If a candidate didn't volunteer the info, I also didn't know. It made zero difference to whether a CV was passed to me.
But, after a hiring campaign had been run, it was possible to see the aggregate of that demographic data. That can be useful in finding out if fewer people of type X are applying for a role, or if statistically more of type Y get a role, etc.
If you showed up to interview wearing a religious garment, while visibly pregnant, dressed in your service uniform, and talked about your experience as a gay immigrant - I wouldn't be able to discriminate against you on those characteristics. But unless I was stupid enough to write that down in an email, it would be hard to prove.
In short, no, it doesn't reflect badly on you and it doesn't impact the hiring process.
Its to see if, if successful there is a selection bias in aggregate
So any information you disclose and becomes known to anyone involved in the hiring process may have a bearing on their decision, whether in a positive or negative way.
Now, bearing that in mind, I expect companies that ask about this want to increase staff "diversity" so use your own judgement as to what answer is positive or negative, everything else being equal.
In some places it is forbidden to use that information against the candidate, though you can never be sure it hasn't been discussed more widely than it should have been. OTOH, do you want to work for an organisation that behaves that way?
I also generally withhold that info.