Doctors should be allowed to give priority to vaccinated patients

Doctors triage patients all the time. The critera are (broadly) how grave is the patient's condition and how likely is it we can help. Beyond that, I'm not sure that any individual decisions or motivations of the patient are of any relevance. Do we want a world where people who don't seek early treatment for any variety of conditions (addiction, mental health, obesity, even cancer, etc) or engage in risky behavior (e.g. many sports) go to the back of the line when they become seriously ill or injured?

Doctors should be able to put fat people on much lower priority.

Worth noting that the "emergency physician" the Washington Post quotes in this op-ed works at CIA front In-Q-Tel: https://twitter.com/LLinecook/status/1434245760455954434

That public health insurance doesn't seem to work in the US is seen in arguments like this, although the article is for generating clicks of course.