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@oromagi
Let's say you're walking down the street and you meet a stranger walking a dog down the street. You say, "Cool dog, what breed is he?" and the stranger replies "Oh, she is a mutt." Wouldn't you effortlessly change pronouns out of common courtesy? If you persisted in calling the dog he the stranger would assume you were suffering from some social deficit and move on quickly. The sick and elderly wish to be extended the same common courtesy in their own bedrooms that any ordinary person would extend a dog in the street. That's it. They don't wish to know what you or Jesus or Rush Limbaugh or anyone really thinks about their identity, they just want you to do your job politely and professionally.
Two counter-points to this:
1) You're assuming a plethora of personal beliefs in "common courtesy". For example, in my homeland of Australia, looking someone in the eyes as you pass them and say "g'day" is normally done amongst white people, but is seriously offensive for Aboriginal people. It's also offensive for any Koreans over here, but it's polite to English people. "Common courtesy" is not a fixed term, as you assume here.
Relating specifically to the topic at hand, let's say a particular culture considers it offensive to call someone a homosexual (perhaps Southern part of the U.S.). Therefore, when someone asks to be referred to as a homosexual, it's going to conflict with what a Southerner would consider "common courtesy", and thus the Southerner is referring to someone else he/she might respect in a derogatory way. Moreover, whose "common courtesy" is correct?
Another specific example to the topic at hand: Aboriginal people considered hermaphrodites to be magical people, and revered them as such. However, I doubt many hermaphrodites would consider themselves to be magical people. So, despite Aboriginal people respecting these hermaphrodites, their "common courtesy", whilst also seeing hermaphrodites as positive, is wildly different to a non-Aboriginal conception of hermaphrodites. Again, whose "common courtesy" is correct?
2) Yes, it could be common courtesy, in a sense of the word, to refer to someone as they request. Personally, unless the person was hostile, I would accommodate his/her request for particular pronouns.
However, a mere request is different from a state imposed threat. The difference is that the person you're talking to essentially has your wallet/purse open, and threatens to steal money from you, in order to give to the government. Imagine that when a person requests that they be referred to in a certain way, that he/she proceeds to open your wallet/purse, and holds several hundred dollars, waiting to see if he/she is allowed to give this money to the government. That is essentially what is occurring.
Imagine you lived your whole adult life as a man until you have an accident and live in a comatose state for 10 years, during which your healthcare providers decide that you are woman in their books and so they dress you in skirts and apply rouge and lipstick to your helpless body. Wouldn't you consider that a humiliating violation?
Referring to someone in a particular way, and physically imposing your will upon someone, are different, and thus should be treated differently.
For example, saying that you prefer to greet people with French kisses, rather than handshakes, is very different from actually forcing a French kiss upon someone, especially when you know the other person not only prefers handshakes, but actively dislikes French kisses. The physicality holds the infringement, and it shouldn't be lumped into mere personal preference/beliefs.