Well, they have to. There is a tradition of conscientious objection. Anyway, the church allows refusal so any Chaplin that refuses to accept that refusal is absolutely wrong. Shame on them, shame on the military for not respecting individual religious beliefs. And shame on soldiers for surrendering their religious beliefs to the military and compromised chaplains.
The Chaplains have no authority to approve a religious exemption. The first Flag Officer in the chain is the decider.
The "tradition" of conscientious objection is discharge.