"That ruling, which was issued last June, decided that the arts-and-crafts retailer, Hobby Lobby, could seek an exemption from the contraception mandate for religious reasons. Since then, religious-affiliated companies and organizations have revived their legal challenges of the provision."
This subPreme ruling may in fact be destroying the right 6to appeal for religious reasons, since the lower court ruled that Hobby Lobby could appeal on religious grounds and scotus evacuated that ruling.
I think you'll find that the Supreme Court's Order in
Burwell v. Hobby Lobby vacated the Decision of the 10th Circuit while affirming the Decision of the 3rd Circuit. The Supreme Court specifically found that individuals who organize their closely held business in corporate form do not surrender their religious liberties by doing so.
While the Supreme Court could have affirmed the 3rd Circuit without an Opinion, the Opinion of the Supreme Court is binding upon all circuits, while an opinion of a Circuit Court is not.