It's that employees of a religious institution who receive healthcare insurance as part of their overall compensation package should NEVER be forced to abide by the strictures of their employer's religious beliefs.
Religious freedom, in this case, isn't the freedom of the employer to behave according to their religious beliefs - it's so their employees aren't forced to adhere to those religious beliefs.
It's actually the basis upon which the First Amendment rests! It's why many members of fringe religious sects came to America - so that they wouldn't be forced to abide by the religious tenets of another religion that they didn't believe in!
This ain't rocket science.
What it is is yet another in a long line of highly manipulated arguments from the right, where they turn an argument on its head. They used this against John Kerry when they turned his vastly superior military record against him, since a fair comparison of his military background with GWB's would show Bush to have been an AWOL fuck-up'd drug user.
In this case, they've twisted the argument to pretend that the religious institutions are being imposed upon, when in fact, if we don't allow individual employees and their doctors to determine what is the best birth control to take advantage of, and instead give their employers the right to veto options on religious grounds, we've denied those women the rights that are guaranteed in our Constitution!
And I suspect that many on the right know this. They fully understand what the "real", traditionally Conservative argument should be on this topic. They realize that if they were true to their roots, they'd have to be on the side of the employee here to be free from the religious strictures of their employee. But they couldn't argue that way, since that's also the way that Democrats would want to go too, just for slightly different reasons. And so they've invented this objection, created this upside-down argument that actually goes against the First Amendment and the right of citizens to be free from coercion. They are eternally hypocrites.
It's not the employers who need to be shielded from "other" religious views. It's the employees who have to be protected against being forced to abide by their employer's religious beliefs, and have those employees remain free to make their own moral and ethical reproductive choices.
Again, it's not rocket science, and so there are certainly Republicans who know, but can't allow themselves to care that they're being entirely dishonest with this argument. They've tied themselves to the extreme right of their party, and they have to placate them or they fear that those voters will rebel and either vote against them for radical third party canidates or those voters will stay home, disgusted.