Attorneys generals from Florida, Michigan, Nebraska, Ohio, Oklahoma, South Carolina, and Texas filed the suit, arguing that the rule violates First Amendment freedom of religion rights and the 1993 Religious Freedom Restoration act. That law, passed overwhelmingly by Congress during the Clinton administration, requires the federal government to justify any burdens it places on the exercise of religion.
. . . in a response last week to a separate lawsuit from Belmont Abbey College, a Catholic college in North Carolina, the Obama administration argued that the suit should be thrown out because the contraception rule is not final.
“The forthcoming modifications, among other things, will require health insurance issuers to … offer contraceptive coverage directly to such organization’s plan participants who desire it, at no charge,” said the Justice Department. “At the outset, plaintiff’s suit must be dismissed for lack of jurisdiction because plaintiff has not alleged any imminent injury from the operation of the regulations.”
Since the rule has not been passed, there is nothing to file suit against no way to know if it is in fact unconstitutional. There is as of yet no standing, on anyone's part, to sue.
In response to the Attorney's General, here's an argument that the new rule fits under existing legal precedence, at least as articulated in Employment Division v Smith back in 1990:
The justices said the First Amendment’s protections do not mean
individuals are free to violate valid laws simply by claiming a sincere
religious objection. To “make the professed doctrines of religious
belief superior to the law of the land” would have the anarchic effect
of permitting “every citizen to become a law unto himself,” Justice
Scalia wrote. The court said the state could exempt religious peyote use
from drug laws, but was not constitutionally required to do so. Under
the Smith case, the administration policy on contraceptive coverage is
clearly constitutional: it is a neutral regulation enacted with no
motive to discriminate against religious interests.
The R.F.R.A. statute, however, uses a far stricter standard. Any federal
government actions that “substantially burden a person’s exercise of
religion,” it says, must advance a compelling interest and be the least
restrictive means of doing so. Even under that test, the new
contraceptives policy should survive legal challenge. It clearly
advances the government’s compelling interest in promoting women’s
health and autonomy, and broad participation is the least restrictive
way to carry out a complicated national health reform.
But courts should not even reach that question since the provision of preventive services without a co-pay does not interfere with a religious practice or ceremony. There is no impediment to the exercise of religion, especially since the administration has revised its original rule, which exempted churches, mosques and other houses of worship — and now also relieves colleges, hospitals, charities and other religiously affiliated groups from having to provide contraceptive coverage directly. The rule does not interfere with church governance, prevent anyone from voicing opposition, or force anyone to use contraceptives in violation of religious beliefs.
Providing contraception does not interfere with an actual religious practice, the author contends, so the religious freedom argument doe not apply.