This post is an oblique response to one of the lines of thought in a petition against Notre Dame University's lawsuit against the HHS contraception mandate.
If your religion or conscience (and on my view of conscience, the former is a special case of the latter if you sincerely accept the religious teachings) forbids you to obey a law, then the law violates your religious freedom or your freedom of conscience. (There is also a further question whether this violation is justified, and I won't address that question.) But the converse is not true. A law can violate your religious freedom, and maybe your freedom of conscience (that's a harder question), even if obedience is not forbidden by your religion or your conscience.
This is easiest shown by example. A paradigm example of a law violating religious freedom is a law prohibiting Christians from meeting to worship on Sunday under pain of death. But obedience to such a law need not go against the requirements of Christianity. Christianity does not require public Sunday worship when such worship seriously endangers innocent life, including one's own. Thus, there is no duty to get to Sunday worship if there is a hurricane, and to get to church one would have to leave the hurricane shelter one is in. Thus, a law that prohibited Christians from Sunday worship on pain of death would violate religious freedom without Christianity holding it to be wrong to obey the law. In case it's not clear that this law violates religious freedom, one can run this a fortiori argument. A law forbidding Sunday worship with a five dollar fine as a penalty would be wrong to obey according to Christianity, unless one is quite poor, and hence violates religious freedom. But if forbidding Sunday worship under pain of a five dollar fine violates religious freedom, a fortiori so does forbidding Sunday worship under pain of death.
For another example, consider a law explicitly prohibiting Jews from meeting to pray together on the Sabbath. It is my understanding that while rabbinical Judaism encourages meeting to pray together on the Sabbath, it does not require this (if I am wrong, just make it a hypothetical example). Thus, this would be a law that it is not wrong to obey, but it surely violates religious freedom.
In fact, one might even have a law that violates freedom of religion without requiring or forbidding the practitioners to do anything. For instance, consider a law requiring doctors who are not themselves Jehovah's Witnesses to forcibly administer blood transfusions to Jehovah's Witnesses when this is medically indicated, even when the Witness does not consent. Such a law violates the patient's freedom of religion, even though the patient is not being required or forbidden to do anything by the law. (The law may also violate the doctor's freedom of conscience.)
It is harder to see whether a law obedience to which does not violate conscience can violate freedom of conscience. There is a prima facie case for a negative answer: How can freedom of conscience be violated by something that doesn't require one to go against conscience?
But I think a case can be made that it is possible to violate freedom of conscience without requiring something contrary to conscience. The cases parallel the above two.
The case of Christian Sunday worship was one where something is required unless there are serious reasons to the contrary. Now, typical vegetarians do not think it is always wrong to eat meat. They would not, for instance, think that an Inuit child whose parents only make meat available to her in winter is morally required to refuse to eat it and thus starve to death. But now imagine a law put in place by the pork lobby that requires everyone to eat six ounces of pork daily, under penalty of death. If it is permissible to eat meat to preserve one's life, it would be permissible for the vegetarian to eat the pork. But surely there is something very much like violation of the vegetarian's freedom of conscience here.
The common thread between the Sunday worship and vegetarian cases is that these are situations where there is a strong duty to go against what the law says, but it is the law's penalty that provides a defeater for the law.
To parallel the case of rabbinical Jewish attitudes to Sabbath worship, consider a Kantian. Now, Kantians believe that there is an imperfect duty to help others, i.e., a duty where it is not specified to what degree and in what way one should help others. Imagine, then, a law that prohibited one from helping others except between 4:30 pm and 5:00 pm on Tuesdays. Such a law might not be such that Kantianism forbids one to obey it. But it is a law that surely in some important sense violates the Kantian's freedom of conscience, by forbidding that which her conscience very strongly encourages her to do, namely help people at other times, even if it does not specifically require it.