I personally don't like the idea of trusting an AI doctor. I know that they probably can make less mistakes than human doctors but still there is no replacement for real humans.
I think trust would build gradually. People are skeptical at first, but if the AI shows consistent results, better outcomes, and fewer errors, public opinion might shift. At that point, relying on AI could feel normal.
There are many different ways to look at the issue, if we just look at it from a point of advancing technologically than it's good, until you realize AI has to learn and the only way it can do so is through trail and error. Which is something it would not be a able to do white working on a live human patient