None. If they don’t want to use contraceptives, that’s on them but they not only have no reason to deny distributing contraceptives, they are obligated and obliged to sell them to people who want them. They can refuse them for themselves, not for others.
How do I know that? By being sentient.
Religions have a special place for most people. That includes giving them special benefits and paying for their existence but they must not be allowed to continue to bully people who don’t share their belief, their faith, or their values. In addition religions and religious people have an obligation to pay for what they get, same as everyone else. There is no Constitutional Right for Religious Bullying in the name of a religion. Freedom of religion does not include the Freedom to Proselytize to anyone. There is no Freedom to Pester Other People.
If they chose not to pay for the benefits they can cancel their business arrangements with the state, privitize and pay for everything they get, same as everyone else. It’s a moral principle that people must pay for what they get. The commandment to not steal only covers half of the issues. The other half is to pay for what you get. Religious people want others to pay but like to exempt themselves. The exemption for contraceptives is a stark example of their hypocrisy at work. They want freedom from taxes but they want the rest of us to pay. They don’t like contraception but refuse to grasp others want it. They want to be free to condemn people who want contraception but they don’t want others to condemn their idea.
Using the same arguments they must perform medical procedures with which they disagree.
They decided to take advantage of government’s gifts to them by going into business. If they don’t want to do what’s required they can re-organize as private clubs, private businesses, private companies or private corporations and join the rest of the community who pay for what they get.