Indeed. Doctors may think of themselves as private citizens, but the services they provide are part of a public service. By elevating the right of the doctor above that of the patient, someone who is less likely to be in a position of access to information or services, you're beginning to replace the rights of one individual for the other.
But while these freedoms may be enshrined in the constitution, they have not fared so well when they have come in conflict with laws passed with an eye toward maintaining order and predictability. In a series of cases stretching from Reynolds v. United States (1878) to Employment Division v. Smith (1990), the Supreme Court has ruled that when the personal imperatives of one’s religion or morality lead to actions in violation of generally applicable laws — laws not promulgated with the intention of affronting anyone’s conscience — the violations will not be allowed and will certainly not be celebrated; for, says the court in Reynolds, “To permit this would be to make the professed doctrines of religious belief superior to the law of the land, and in effect to permit every citizen to become a law unto himself.”
It could be said that such language is too melodramatic for the current dispute, which does not involve disrupting the machinery of government, just the granting of exemptions from some professional obligations. What’s the big deal, for after all, “If a procedure is legal, a patient will still have the ability to access that service from a medical professional or institution that does not assert a conflict of conscience” (HHS News Release, August 21, 2008).But should patients be asked to add to the problems they already have the problem of having to figure out (if they have the time) which providers will be willing to treat them? When a professional hangs out his shingle doesn’t he offer his services and skills to the public and not just to members of it who share his morality? Isn’t it a matter of conscience (in Hobbes’s sense) to abide by the rules that define the profession you’ve signed up for?
The important thing to remember, though, is that even though it looks likely that HHS will rescind the so-called conscience rule on the federal level, other states have already codified such conscience rules into their state laws. Illinois is just one of many.