For starters, they are moral person. Every corporation, institution, nonprofit and what have you is a moral person. We don't mean moral in the sense that they necessarily act morally. But they have a certain individuality, an existence of their own, and as such must be treated as persons. Especially as persons run them, it strikes us as quite logical that they have the same responsibilities, and therefore rights) as flesh and blood people. They're simply expressing themselves in a different, less direct, medium.
This means that their religious sentiments, again, where reasonable, may be expressed through their policies towards both their workers and their societies. If they don't want to pay for their employees' birth control on religious grounds, and especially as sex is a wholly voluntary action, then they should not have to as a matter of moral and constitutional right.
But that won't happen. Common sense, let alone any sense of the Constitution and religious freedom, mean little these days. Our nation has lost its moorings and is adrift on a sea which will take it with the currents. That they will take us somewhere somehow is certain. And we will be further and further from our moral dock as time goes on.