To what extent can the religious demand that non-believers obey the religion
This is a genuinely tricky issue because each religion has dictates that are indeed accepted by those who are not adherents of the religion. For example, almost all religions prohibit murder, and nonbelievers generally also reject murder, so there is considerable overlap among the various religions and also the nonreligious for this particular dictate. The same goes for theft and adultery.
But when the religious belief requires, say, eating only a vegetarian diet, do members of the religion have a right to demand that nonmembers discontinue the eating of meat? Or would Jews and Muslims be right in forbidding Christians to eat pork?
I think most would say no. And yet the Catholic church will do anything in its power to prevent non-Catholics from using birth control, up to and including letting HIV continue to spread and kill people (as in the case of Africa, where the Catholic church has fought to prevent the use of condoms). And those whose religious beliefs require them to not use abortion seem determined to force even those who do not share that belief to obey it, despite the legality of abortion in this country—a country in which many believe an abortion is a matter of individual choice.
In the case at hand a number of people are determined, based on their own religious beliefs, to prevent company insurance plans from providing perfectly legal contraception services to those who do not share the religious beliefs. Their beliefs (in their view) are that it is not enough simply for themselves to adhere to their religious dictates, others must obey as well.
The only saving grace is that these same people observe the principle of reciprocity and they themselves adhere to rules imposed by other religions—for example, the people demanding that others not use contraceptives or abortion are willing to eschew meat (and particularly pork), pray 5 times daily in the direction of Mecca, and so on. Since they demand that their religious beliefs be imposed on others, they themselves are willing to accept the imposition of beliefs from religions that they do not hold. Oh, wait…