Sometimes. In Burwell v. Hobby Lobby Stores, Inc., the Supreme Court held in a 5-4 decision, that closely held corporations whose owners are religious cannot be required to pay for contraceptive coverage. In deciding this case, the Court made a statutory, not constitutional, interpretation of the Religious Freedom Restoration Act (RFRA), explained above.
The Court held that a closely held corporation is a person who can exercise religious beliefs under the RFRA; that the birth control mandate under the Affordable Care Act puts a substantial burden on the company's religious beliefs; and there are other less restrictive options to achieve the Government's objectives without interfering with the company's religious liberties.
Recently, the United States Supreme Court decision in Little Sisters of the Poor v. Pennsylvania, allows employers to refuse to provide health insurance that covers the cost of contraception if they have a religious or moral conflict. After this decision, employers who do not provide contraception benefits because they are exempt from doing so due to religious or moral conflicts, will not be committing discrimination.
While many questions relating to this case are still arising, this case essentially stands for the notion that a company can have sincere religious beliefs and based on those religious beliefs can eliminate the right for female employees to access contraceptive coverage through employer-covered health plans. Although the Hobby Lobby case was about insurance coverage for contraception, the decision opened the door for many state RFRAs to be used as tools for religious exemptions.