The Reasonableness of Refuse-but-Refer
Whether the "refuse, but refer" policy is "reasonable" I think depends a lot on what the nature of the religious objection is. "Refuse, but refer" makes perfect sense if the objection is a personal one: 'I the conservative Christian don't like, and am morally squeamish about, abortion. I don't want to perform an abortion because that would damage my own holiness and relationship with God.' This is the kind of situation Hilzoy is imagining when she raises the hypothetical of "if one of thirty Ob/Gyns in a large hospital believed that it would be wrong for her to perform abortions" (emphasis added). Liberals, particularly those of a secular bent, have a strong tendency to want all religion to operate in this personal mold -- a desire which often spills over into thinking that all religion does in fact operate in this mold.
It would be highly convenient if religion was all personal in this sense. It would make it easy to achieve a purely procedural accommodation and tolerance between divergent substantive views. That, I take it, is what Jill means by calling the current situation "reasonable" and what is communicated by the bumper sticker that says "If you don't like abortion, don't have one." This desire to agree on laws without having to answer any major substantive questions is the heart of traditional philosophical liberalism*.
But not all religion is personal. Some of it is consequentialist -- believers see themselves as called not to engage in certain personal practices for individual salvation and holiness, but to promote good and attack evil in the world. If one has a consequentialist objection to abortion, one's concern is not 'I don't want to perform abortions,' but rather 'I don't want abortions to be performed.' Thus, a "refuse, but refer" policy is cold comfort. While referring an abortion-seeker to another doctor may give a little psychological relief to the consequentialist conservative Christian, an abortion performed by another doctor is just as bad, in God's eyes, as one performed by the refuse-and-refer-er. The same number of fetuses is being killed. Personal refusal to participate is useful only as a mechanism for stopping the practice from occurring at all.
If some substantial number of conservative doctors has a consequentialist, rather than personal, objection to abortion -- and I think this is so -- then no liberal tolerance compromise is available. The substantive question -- is abortion a service that people are entitled to get from any health care provider? -- must be faced head-on. If the "yes" side wins -- and I think it should -- then anti-abortion doctors will have to either accept the requirement to do something they hold to be wrong (either directly or by culpably delegating the responsibility to someone else), or get out of the medical business. And those of us pushing for the "yes" side to win must be cognizant that this fight is over a substantive issue, not over whether a personal belief is to be accommodated or overstep its boundaries.
*Liberalism may try to get around this by decreeing that to be acceptable, religion must be private. This would allow the liberal project to move forward -- but at the price of an arguably illiberal law that strongly restricts the range of application of liberalism's vaunted tolerance. This is one of the more troublesome aspects of Rawls' theory, to my mind -- his breezy declaration that he was limiting himself to "reasonable" substantive doctrines tends to disguise how narrow the range of accepatble doctrines is, as many of the ones found in our actual society would not meet Rawls' criterion of reasonableness.