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Anonymous
The ambulance driver analogy fails because nobody is arguing for a right to refuse to treat a patient because she's had an abortion (or performs abortions). Rather, they're arguing that doctors should not be forced to perform or refer for a procedure if it's not medically necessary and one they don't consider to be good healthcare. More on the mark would be refusal to perform a permanent sterilization, circumcision, virginity test (or hymen restoration), conversion therapy, lobotomy, or genital mutilation of an intersex individual. Even with ordinary, non-ethically challenging situations physicians often exercise their right to refuse - for example, antibiotics are sometimes withheld (if they're not necessary, in order to prevent antibiotic-resistance) and eye surgeons sometimes refuse to perform refractive lens replacement surgery on people that don't actually have cataracts (as the benefits to the patient aren't sufficient to justify the risks).
It would be reasonable for a doctor in this type of situation to refer the patient to a different doctor for a second opinion (someone who may or may not decide to perform the procedure based on her own medical assessment and view of whether the procedure constitutes good medicine), but it would be wrong to force the first doctor to do it herself or pinpoint exactly where the patient would be guaranteed the procedure in question. Interestingly enough, very few abortion practitioners (if any) are willing to perform abortions throughout all nine months of pregnancy. Thus, they exercise their own right to refuse. The question is then whether every doctor should have this right, or only the most abortion-favourable doctor in a given region.
As for why abortion advocates come out against conscientious objection, it clearly has nothing to do with making sure women can access abortion (though making that argument, they imply that they think women are too stupid to find an abortion clinic on their own). Every time they've been asked to prove in court why it's necessary to require the referral, they've been unable to come up with any actual example (appealing instead to vague hypotheticals). Notably, this came up in the landmark NIFLA v. Becerra Supreme Court decision (which was resolved in favour of the pro-life clinics, thankfully - a good example of American exceptionalism and why people from around the world come to the US for religious freedom). Rather, the real reason is to further marginalize pro-life people and drive them out of healthcare professions. Joyce Arthur, leader of the Abortion Rights Coalition of Canada, has made a total ban on conscientious objection one of her main hobby horses. She makes clear what it's really about:
"[Conscientious objection] in reproductive health care is actually a reflection of stigma against abortion and women’s autonomy, not CO in the true sense of that term. It is an attempt to claw back the legality of abortion and return women to their traditional roles of wife and mother, producing soldiers and citizens for the state. We also see it as a form of revenge by organized religion for its loss of power in a world dominated by democracy, self-determination, and evidence-based science and medicine."
https://rewirenewsgroup.com/article/2014/05/14/why-we-need-to-ban-conscientious-objection-in-reproductive-health-care/
(yes, she thinks the pro-life movement is really about pumping out soldiers for the state. She's pretty far out there, but that's for another day)