Trust in what sense? With computer security? You probably can't. To diagnose you and find a proper course of treatment? You probably need to research the individual doctor.

My mother worked at a hospital for years helping doctors use computers to keep up to date with research in their fields. By and large, doctors 10-15 years ago sucked at using computers. Doctors who helped save the lives of relatives of mine by diagnosing cancer early would struggle doing simple searches.

I knew a psychologist who would openly chat about patients - names included - in casual party settings. Doctors don't have to be bad at computers to violate your privacy.

If you think their computer security could be better, you're right, but the more they have to learn, the more room for error you're introducing during the changeover. Do they spend millions replacing a diagnostic machine because no one knows how to switch it to better software? When it works and those millions could go towards equipment that needs replacing?

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5996174/

My suggestion is to do research on tech security in hospitals. Read up from people who are experts in the subject, because it's deeply complicated. Figure out what current recommendations are and contact your local doctors and hospitals to find out if they're investing in patient information security. They might still not use linux, but it's more important they be doing what research shows works.

When you find doctors and hospitals that are working towards those recs, give them what trust you can muster, keeping in mind any of them could just be like "my lung cancer patient Joe Smith said the funniest thing yesterday" at their next cocktail party.

Most won't. But these are human run systems. You need to give them enough trust that they can monitor your health, but be prepared to withdraw it when they prove it's undeserved. Tech-wise, pay attention to actual recommendations from experts and keep in mind that the doctors themselves aren't the experts there.

Just, like, don't let yourself die because your doc thinks a linux is a kind of hybrid animal.