I am having some health issues and unable to see my PCP. So I took the next available appointment with "Dr. Smith". It turns out that Dr. Smith is a They/Them.
It is hard for me to take these people seriously in any context, but especially one where they are making important decisions that impact my life and health. I know that many of them are intellectually smart, they are just brainwashed / captured and may have helpful medical advice. Rescheduling is not an option.
I would not. I would not trust a medical professional who does not believe in science. It would not matter whether they were male or female.
If this is urgent, then I would just suck it up and see them. But otherwise, I would cancel and ask for a different doctor. I would find it really hard to trust their medical opinion and I wouldn't want to gaslight myself into thinking otherwise.