This is one of the consequences of corporate personhood. Now companies can claim religious beliefs. Supposedly, the ruling is narrowed to "closely held" companies, but there are lots of those in the US.
Here is a concise summary from Vox.com.
Today's Supreme Court decision against Obamacare's birth control mandate comes in at at a hefty 49 pages (95 if you count the three dissenting opinions). If you're looking for a more pocket-sized version of the ruling, here's the decision summarized in three key points:
(1) A federal law called the Religious Freedom Restoration Act was written to protect individuals' religious freedoms — and on Thursday, the Supreme Court ruled that, under RFRA, corporations count as people: their religious freedoms also get protection.
(2) The requirement to cover contraception violated RFRA because it mandated that businesses "engage in conduct that seriously violates their sincere religious belief that life begins at conception."
So SCOTUS has made an equation: business = family. A family-owned business that employs people can now inflict the family's religious beliefs on the business' employees.
(3) If the federal government wanted to increase access to birth control — which they argued was the point of this requirement — the Court thinks it could do it in ways that didn't violate religious freedom, like taking on the task of distributing contraceptives itself.
Harry Reid promises legislative action on this point, but will the Tea-Party-dominated House go along?
The Supreme Court also put some restrictions on who its ruling applies to, saying ruling that only "closely held" corporations can be protected under RFRA, the religious freedom law. Since about 90 percent of companies are, however, closely-held, its unclear how much of a difference that distinction makes in the ruling's scope.
So Justice Ginsburg was right in her dissent - the ruling is startling in scope.