I'm vaccinated, so if I found out that was the case at my dentist (and it very well might be), I wouldn't love it, but I probably wouldn't try to find some other dentist. My wife left our dentist because she was pissed at them about something, and hasn't found a better one yet. I've stuck with them so far and am satisfied, so I wouldn't be bothered enough by it to bolt them after 20 years. I certainly never considered trying to find out. They're all pretty wrapped up in masks and face shields. I went to them before vaccines were out and wasn't that worried about it.
It would reflect badly on them as far as intelligence or whatever, but they aren't scientists. All they ever do is clean my teeth, and it's not realistic for me to act like you need to be scientifically brilliant to scrape my teeth.
However, if I was having complex surgery, or being advised to have complex surgery, knowing the surgeon didn't believe in vaccines would give me pause about their general competence and expertise. I wouldn't be too worried about catching COVID, but would be worried about taking medical advice from someone that doesn't believe in vaccines.