Its tricky to figure out who it is ok to ask - I would have thought there would be a market for people who advertise themselves as being vaccinated, so maybe you could try and seek out people who make it clear they are?
As others have said, it absolutely lowers chance of transmission, even if it doesn't remove it, which is a good thing.
As an employer, I'd like to know simply because it helps risk assess: however I do think on principle it makes more sense for only a v small cohort of employers to be allowed to know and a smaller cohort of employers to make a vaccine mandatory, i.e. healthcare and care workers. I know because staff members have taken time off to get their vaccines and mentioned it but I appreciate mandatory disclosures are problematic.
Someone who hasn't had the vaccine because they're concerned around fertility/brain tumours - well, I wouldn't love it, but I don't think the risk is huge. However I guess if I knew I'd try and make sure they didn't clean the room I was working in, rather than just nipping out for a walk/timing their arrival for my lunch break. Personally however, I would be v wary having someone vocally anti-vax all over social media in my house because my assumption is if they believe covid is a hoax they're taking absolutely no precautions in any settings.
The funny thing is, I'm pregnant and talking to my GP lately about how low the rate of take up is among pregnant women realising the most 'at risk' place my baby and I are likely to be in the next few months is the public maternity ward. There's basically nothing to be done about some situations.