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In 1918, the Southern Baptist Convention produced a Resolution on Chaplains that called on the US Congress to abolish chaplaincy and allow denominations to serve soldiers independently:
THEREFORE BE IT RESOLVED, By the Southern Baptist Convention assembled, [...] that the Congress of the United States be memorialized to consider the propriety and rightfulness of abolishing the Army Chaplaincies leaving the religious services to the discretion and election of the different Christian denominations.
They affirm the importance of sharing the gospel with soldiers, but argue that "[r]eligious liberty cannot be absolute where any of its appointments or appropriations are by authority of the state." They also note the expense incurred by the government by paying chaplains.
They would replace state-sponsored chaplaincy with voluntary provision of religious services by each denomination, claiming that "[t]he different Christian denominations of this republic can and would send voluntarily through their agencies, religious teachers to all departments of the army and navy."
It does not appear that the Southern Baptists prevented or prohibited their members from entering the chaplaincy, so this is simply an example of general objection to military chaplaincy, not necessarily a condemnation of those working as military chaplains.