If we look specifically at the Christian tradition, priesthood was generally the occupation of the second born son, but due to high childhood mortality both sons would be tutored in handling a sword incase the first died. The concept of a warrior monk is sound.
Nobody is arguing that you cannot have a religious warrior. Warriors can occupy Elder ranks in a religious hierarchy and be given religious titles.
The priest class is not about your position in a religion, it is about how you occupy your days. If you fight battles, then you are a warrior. As Indirik says, you do not have to remain warriors forever; there are many characters who are played as priests on most occasions, but who switch to warrior during important wars while keeping their religious rank and RP, and that's fine.