It appears that HL wins its case -- closely-held corporations cannot be required to provide contraception coverage because the RFRA applies to regulations that govern the activities of such en ies and the government failed to show that the ACA mandate is the least restrictive means of advancing its interest in ensuring cost-free access to contraception. Apparently, the opinion is highly-qualified; as the SCOTUSBlog people are saying: the opinion "concerns only the contraceptive mandate and should not be understood to mean that all insurance mandates, that is for blood transfusions or vaccinations, necessarily fail if they conflict with an employer's religious beliefs," and "does not provide a shield for employers who might cloak illegal discrimination as a religious practice."
Notably, Justice Kennedy in a concurring opinion says that the government could pay for the coverage itself.