A church isn't a business, nor is it built on refusing to follow court orders. A clergyman doesn't have to violate a court order to protect someone's confidences: he can invoke a legal privilege that's creates an exception to the general subpoena power. The same is true of a lawyer or a spouse. They don't have to violate the court order--they are protected by special exceptions to the rule. They simply need to invoke the exception in a motion to quash.
In general, however, a business will not be protected by any evidentiary privilege. In order to avoid complying with a court order, they will have to violate it.
Did you see the "in their judgment" bit? (Or the "not technically a business" bit, for that matter?) A court can still order testimony if the judge feels it doesn't qualify for the immunity, even as the priest feels that his duty is to protect it.
You can't dismiss the scenario by acting like a priest will never protect a confessional in violation of a court order.
In general, however, a business will not be protected by any evidentiary privilege. In order to avoid complying with a court order, they will have to violate it.