Just a couple of things...
#1 Do you support the right of individuals to claim a "moral conscience" (whether you disagree with it or not is irrelevant) and to hide behind that to discriminate against Blacks, or Mexicans, or Jews, or Women, or the disabled (remember the Muslim cab drivers refusing to take disabled people with service dogs?)? (Personally I support the repeal of Public Accommodation laws so not "moral conscience" requirement would exist because as a private business they have rights of property and association that are usurped by PA laws.
#2 It's a matter between the employee and the employer if an individual refuses to perform their duties.
#3 I agree that religious organization should be able to operated based on their own principals (as long as the comply with basic heath and safety codes), that does not mean that they can expect to receive a contract from the state if they function in a discriminatory fashion. Boston Catholic Charities is one of the more famous instances. Some people assume that Catholic Charity adoption was shut down in Massachusetts, that is not correct. There are still plenty of Catholic Charities in MA that provide adoption services. The thing with Boston Catholic Charities is that they were under a $1,000,000 contract to the City to fund their services. Boston Catholic Charities was not forced to close their doors, they choose to close adoption services when they were told that if they were going to accept taxpayer funding then they could not discriminate against taxpayers.