My view is, it is appropriate to call one a "doctor" in a healthcare setting if your licensing board requires the minimum entry degree to be the doctorate. In this case, that absolutely includes psychologists. I always tell people "psychologists are doctors too." I do a lot of advocacy work to clarify with folks that most state boards have provisions who can use the title "psychologist" as a stand-alone label, and that means those who are independently licensed psychologists. If you are a social, developmental, cognitive psychologist, then they can use those labels, but they must include their respective research area such as social, cognitive, etc. Otherwise they are violating state law. And that is enforceable.
If we don't advocate for ourselves, we become less and less irrelevant. Some folks don't care, but I do. I didn't work my butt off to be viewed by my colleagues as a "second class" doctor, or not even a doctor. I think one other member also mentioned that the title "doctor" is not just allocated to physicians, but podiatrists, psychologists, dentists, pharmacists, etc. What needs to be enforced and protected are each respective fields such as physician, pharmacy, psychology, etc.