It's mostly a non-issue for me, and I'm pretty matter-of-fact about it. They need to know, so I tell them. But I had a mammogram recently, and the woman who called me back for the test got very confused when I stood up, and she kept questioning why I was there -- thicker than a brick, she was. I didn't really feel like outing myself in the middle of a crowded waiting room, so that was a bit annoying. But they sorted it out, and after that everyone was very respectful.
With a small sample size, we already have some pretty different answers, so maybe there's a need for this. But, AnonyMs, I think you're right that there's a built-in response bias against people who are seriously stealth.