I am one of the signatories of an amicus brief by Catholic theologians and ethicists in the Gilardi case against the HHS contraception mandate. The DC Circuit Court recently ruled against the HHS in this case. The main line of thought in our brief was that a Catholic employer's providing coverage for contraception makes the employer cooperate in the employee's use of contraception. Now, Catholic moral thought not only takes (marital) contraception to be wrong, but also takes cooperation in someone else's sin to be morally problematic. Whether the cooperation is not just problematic but wrong depends on questions about the degree and kind of cooperation involved.
Reflecting on these issues makes me think there is a second really crucial thing going on, besides making employers complicit in employees' sin (and we touch on this in the brief, though I think it can be developed). One of the reasons for the HHS mandate is precisely to encourage women to use contraception (this is certainly not denied). But this means that the employer is made complicit in what the employer conscientiously takes to be the government's morally wrongful promotion of wrongdoing. And this cooperation is even closer, and thus far even more morally problematic, than cooperation with the employee's use of contraception. For the employer here acts as the government's instrument in its policy of promotion of contraception. Note that promotion does not require success: in this case, governmental promotion of contraception occurs whether or not any employees actually use the contraception.