Religious organizations shouldn't have to cover contraception. Agreed. That should apply to religious-run churches, monasteries, universities, and hospitals.
But the nuns even objected to filling out a form stating they are a religious organization. How is that any different than filing for 501(c)(3) tax-exempt status?

Second, there is a concerted movement to place pharmacist's assistants who have religious objections to contraception in pharmacies that dispense it. Then, when the pharmacy fires the assistant for failing to perform their duties, suing the pharmacy for religious discrimination.
You want a one-way street for religious freedom.
You want all the power on the side of religion.
Orthodox Jews don't work at BBQ joints that serve up pork.
Why insisting on the right to work at a pharmacy that dispenses contraception and then refuse to fill the orders?