It's interesting to see the divides in attitude this exposes among people who traditionally would have appeared on the same side on political questions. I'm inclined to agree with those who are against mandatory vaccine passports -- in particular because, as NJ points out, it's odd to mandate having something that isn't actually mandatory under the law and currently cannot be; as well as because having to declare one's medical history to the State on matters of "choice" is in violation of a right to privacy. I don't agree that this would be the start of any slippery slope or mission creep, but it would almost certainly be subject to a successful legal challenge.
As a separate point, since people who are vaccinated can still catch the disease (albeit less seriously, hence the importance of getting a vaccine), and since it's generally recognised that people who are fully vaccinated can still spread Covid (see, eg, latest CDC guidance), then this restriction doesn't even seem to address the problem it's meant to. In that sense, the only demonstration that you don't pose a risk of spread to others is through an up-to-date negative test.