Catholic For a Free Choice campaigns for abortion; it has been condemned by the US Catholic Bishops' Conference; see the information here. It is currently seeking to undermine the role of 'conscience clauses', clauses in laws or contracts of employment which allow anyone with an objection to abortion to refrain from cooperating in it. They make an extended argument in their pamphlet 'In Good Conscience: Respecting the Beliefs of Health-Care Providers and the Needs of Patients', available here.
The argument can be summarised as follows:
1. Conscience is sacred.
2. When a doctor/nurse/pharmacist declines to hand over pills/perform an operation which a patient desires (presumably in good conscience), the patient's conscience is 'negated' (p12). There ought to be 'deference to the conscience of others' (p9).
3. Doubt is cast on the possibility that the medical employee is himself acting in good conscience, by suggesting that in refusing to hand over abortifacients or perform abortions they are merely following the orders of their Catholic hospital or of the Catholic hierarchy (p.10).
4. Even if the conflict between the patient and the medic can be seen as a conflict between two consciences, the way to resolve the matter is for a Catholic (or any other) hospital to 'serve as a facilitator of all consciences': i.e. to let the conscience-afflicted medic to step aside from the case and replace him with a more flexible colleague. Presumably the original medic's cooperation here will be required (p.13).
From a Catholic point of view (the document is at pains to present itself as based on Catholic principles), this argument is bizarre.
On (2): conscience relates to the agent's actions, or to what they ask or agree to have done to them. If a woman (sincerely, conscientiously) wanting an abortion is refused one by a Catholic doctor, this is not parallel to the situation of a (sincere, conscientious) doctor whose employer seeks to overcome his reluctance to perform abortions by threats. In the latter case, an attempt is being made to get a person to act against his conscience; in the former case, one free agent is declining to cooperate in the proposed action of another free agent.
CFFC's refusal to see the doctor as a free agent in this situation is puzzling. The suggestion seems to be that since the doctor has the knowledge and the equipment necessary for an abortion, he is under an obligation to perform one to anyone who asks. But no doctor is under an obligation to give patients the treatment they ask for: it is the doctor's role to determine what treatment is appropriate; the role of the patient's conscience is to refuse to submit to treatments the patient thinks are wrong. The patient may be deluded or obsessive about his medical interests; in the case of abortion, the conscientious Catholic doctor will not conclude that abortion is in the interests of either the mother or her unborn baby.
On the one hand CFFC wants to say that abortion is simply part of normal medical treatment; but on the other hand, they are claiming that it has a special status in which the patient, uniquely, takes the initiative and the doctor is a mere technician who must obey or risk violating a right. But the mere fact that abortion is legal under certain circumstances does not mean that anyone has a 'right' to it.
On 3. There is no reason to suppose that Catholic medics who pay attention to the Church's teaching are not thinking for themselves. In a society where abortion is commonplace and socially acceptable, anyone who is reflective enough to accept the Church's arguments, based on Natural Law, against abortion is taking a courageous stand against the current. The role of Church teaching in clarifying our thinking on moral matters is part of the development of the 'formed conscience', a phrase absent from CFFC's discussion. This is obviously what Church teaching is for: what else is it for? On the other hand, the conscience of women who ask for abortions may well be distorted by the refusal of secular society to think the issue through, and above all by pressure from family and friends. This is not a good example of a conscientious decision.
On 4. First, a medic who, faced with a request for abortion, calls in a colleague to carry it out, is cooperating with abortion. If abortion is wrong, then this is wrong. If a hospital asks him to do this, it is asking him to act against his conscience.
Second, hospitals exist to further the health of their patients. If a hospital chooses to reject that role, and become places where women can dispose of unwanted members of their families, they are not being 'neutral' about anything, but evil. Such a hospital clearly could not call itself 'Catholic'.
In summary: it is never right for any doctor to give any patient treatment which the doctor thinks will harm the patient (unless a medical intervention is necessary to help for example an unborn baby), however sincere the patient might be in asking for it. It is also wrong for any doctor to arrange for such treatment to be given to the patient by another doctor. Equally, it would be wrong for any doctor to give a patient treatment which the patient refuses to consent to. To override the doctor's judgment or the patient's consent by coercing them to act or be treated against their wishes is to violate their autonomy and freedom of conscience. This has got nothing to do with religious belief; these are principles of Natural Law which protect the consciences of everyone.