Without regard to whether the enabling statutes cited provide this authority, I see some significant legal problems.
1) I do not believe this case falls into the "Rust v. Sullivan" subsidy line of cases, as expanded in Legal Services Corp. v. Valasquez (text here). As subsequently modified, Rust addressed only whether the government could ensure that its message was not confused with other messages. Here, the government places a restriction on a core function, the same fatal problem found with the restrictions at issue in LSC. Just as providing legal advice on issues of public housing is longstanding critical aspect of rendering legal services, teh ability to rely on employees to provide the full range of medical services is a core aspect of medical institutions.
2) The structure of the regulations provides an added level of protection over and above those awarded to other religious practitioners and beliefs. Under employment law, all religious beliefs are subject to the limitation of bona fide occupational qualifications (BFOQ). That is to say, an employer can refuse to hire or accommodate someone whose religious beliefs make it impossible for him or her to fulfill a critical aspect of employment. Thus, a hospital open 24/7 may refuse to hire a Sabbath observant pharmacist or EMT because that person refuses to work on his or her day of rest, even where accommodation may be possible. The employer is under no obligation to place added strain on the other employees, because all applicants know that the ability to work on a 24/7 basis is a critical aspect of health care.
Generally, the requirement that a health care provider may rely on all staff reliably to carry out any needed medical procedure or fill any medical prescription is a BFOQ. While case law in this area remains uncertain, the overall consensus is that the employer is not required to accommodate the religious belief of an employee who refuses to perform, participate in, or otherwise facilitate a necessary procedure. The problem is of increasing difficulty the broader the range of behavior that falls into the "conscientious objection" of the employee. Is it legitimate for a nurse, for example, to refuse to attend any procedure that _might_ end in the termination of a pregnancy? Can a technician demand to know the case history of a patient before transporting a patient from point A to point B to ensure that s/he is not somehow facilitating a procedure the employee would find a violation of religious belief?
Given the language of the proposed rules, which speak in terms of "religious discrimination" and "religious belief," it cannot be doubted that the intent of the government is to confer protected status on the basis of a religious ideology. While neutral to the extent that it is open to any religion that respects the "sanctity of life" in the manner described -- and thus could apply to a variety of religions and religious sects -- it privileges one particular set of beliefs over all others. That is, only a religious belief with regard to the "sanctity of life" as applied to the termination of a pregnancy or a barrier to conception is exempted from the standard BFOQ limitations of employment law.
It is certain that the government can protect against discrimination on the basis of religion, when done in a neutral manner. Under the commerce clause, the government is free to establish any neutral criteria as a protected class. Thus, the government may prohibit discrimination on the basis of race, national origin, age, or physical disability without running afoul of the Fifth Amendment, and may likewise prevent discrimination on the basis of "religion" generically. In doing so, it should be noted that the prohibition on "religious" discrimination would likewise apply (to avoid and Establishment Clause issue) to the absence of belief. Thus, refusal to hire someone because someone is an atheist (where religious belief is not a BFOQ) would also violate the laws prohibiting discrimination on the basis of "religion." Any other result runs up against the Establishment Clause.
The regulations at issue are not neutral in this manner. They address only one form of religious or moral obligation -- to the exclusion of all others. In doing so, the government establishes a particular religious belief, the "sanctity of life" as defined by the regulations, as a superior belief to all other beliefs. Although this belief is shared by many religions and philosophies, that does not make protection of this specific objection -- as opposed to, for example, observance of the Sabbath as a day of rest, refusal to use blood products, or refusal to handle materials derived from pig or other "impure" animals -- neutral in the legal sense.
At least, in my opinion.