Catholic Church on Birth Control

It is not that the Catholic Church has a problem with women wanting to use birth control, they just have a problem with providing it to women.

Sister Carol Keehan is president of the Catholic Health Association, which oversees more than 600 Catholic hospitals. She says no one is turning patients away, and in fact the vast majority of Catholic women use birth control and want coverage.
- NPR

The Catholic Church wants the right to deny birth control for women, even though they admit that most of their own want it.

Romney has lept at the chance to use it as a talking point in his bid for the presidency, saying "We must have a president who is willing to protect America's first right — a right to worship God according to the dictates of our own conscience," (Source: NPR). I have to ask, however, what is to be done when the rights to worship God according the dictates of someone's conscious interferes with the  rights of another to make healthcare decisions for them or their daughter?

Is it really the place of the Catholic Church to tell a women that their employer will not pay for birth control so that she can live a normal life, free of the pain of endometriosis? And yet the Catholic Church happily provides men with Viagra because they say that it helps to make more babies.

Does the Catholic Church only hire Catholics to work in their hospitals? What about equal employment rights?  And if they do hire non-Catholics, than why are they wanting to impose their religious point of view on their non-Catholic employees? What about the right of freedom of religion?