Yes, religious organizations should be exempt from work discrimination laws regarding gender, because they have religious reasons for wanting to employ certain people in certain positions. It is no different than needing a woman to run the National Organization of Women. They should be allowed to choose who suits their needs.
Religious organizations should be exempt but only in situations where such practices are required by religion. This would require that a court at some theoretical point would be tasked with the interpretation of theology - an unpleasant notion, but it would at least respect the practice of religion while not allowing for other discrimination.
I definitely think that religious organizations should be exempt from work discrimination laws regarding gender. I think that religious organizations operate on a different set of rules and beliefs. They should not have to be made to hire somebody to a certain role if it does not match their beliefs.
Both women and men are supposed to be legally equal before the eyes of the law. If we allow religion to violate these laws, then a) we are allowing/encouraging them to engage in human rights' violations, b) we are sending the message that it's okay to discriminate against that sex (or against that sex under those circumstances), and c) the person who they are discriminating against, their basic rights are not being upheld, and d) we are actually putting the religion above the law in that case. Would people be okay if we said 'oh hey, let's not prosecute crimes that happen in religious buildings?' and let off say, thieves, murderers, and pedophiles who used religion as a way to hide their crimes? No. Discrimination based on sex is illegal. We wouldn't put up with a religion that said 'no, we won't hire people of a particular race' either. Religion is a choice, someone's biological sex (or race) is not.
Discrimination in the work place is unacceptable in any organization. I believe there is a distinction between being a volunteer or being in an unpaid spiritual position, but paid workers deserve fair treatment across the board. If it is morally and ethically wrong to discriminate in a non secular organization then, logically the same is true in secular organizations.