My default is to call anyone who has earned a doctorate degree "Doc" - it is a respect thing.
As a provider myself, I always call others by their professional title - unless they tell me otherwise or I also know them as a friend. For me, it's a matter of respect; similar to addressing Officer Smith instead of simply Cathy or Bob. Our relationship is professional and it helps maintain a certain level of interaction in a relationship that involves rather personal details.
You should use singular "they" here. "He/she" is out.
I've worked with physicians for over 25 years in healthcare IT. For some reason, I've never been comfortable calling them by their first name, even when we're working as coworkers. Funny thing is that I've never referred to any of my current or previous bosses by Mr or Mrs/Ms.
I always address patients using “Mr/Mrs\etc” and they almost always call men”Dr” back. I introduce myself as “Dr”. I trained in the late 90’s but to me it just sounds weird in the exam room. Also helps keep some professional distance.
Perhaps it’s because I trained in the early 1980s, but I was taught always to refer to patients as Mr, Mrs,, Ms, or Dr. depending on their formal title and they would generally call me Dr as well. If a patient requested that I call them by their first name instead I would do so. Because of the context in which I work, there are some patients who call physicians derisively by their first names in a clear effort to be intimidating. And when that happens, we redirect them to use our professional titles. In other contexts, I have no concerns if a patient who I know well calls me by my first name. When I see physicians myself, I almost always refer to them as Dr regardless of whether they are younger or older than I am. I am counting on them to treat me based on their professional judgement and experience. I’m not seeing them because we’re friends. (Paradoxically physicians and their families often get worse care than other patients because treating physicians and staff don’t ask the hard questions.). Regarding the issue of client vs patient, I firmly believe the relationship between a physician and patient has additional elements and ethical responsibilities beyond that of a typical client. But it wouldn’t occur to me to call my attorney by his or her first name either.
I am the client of my PCP (or any doctor). They are working for me not the other way around. If any doctor told me I had to call them Dr. I would walk out (if I was able to).