Are there any non-pacifist traditions that object to military chaplaincy? I'd like to know if there are any non-pacifist Christian traditions or denominations, either historical or contemporary, that object to individual participation in the military as a non-combat chaplain, or to military chaplaincy in general.

I see several possible reasons why Christians might not serve as chaplains:


A view of pacifism that forbids any connection with the military
A view of the state that forbids association with the military in this particular capacity (e.g., concerns over state establishment of religion)
Moral opposition to a particular action that is required of chaplains (such as performing same-sex marriages)


I'm most interested in #2, but also #3.  I imagine that there are multiple examples of #1, but that's another question.

Regarding #3, I'm aware that there is ongoing fighting in the U.S. between Christian groups and the Pentagon over what chaplains can and can't do.  I'm not looking for an example of one that is fighting, but one that has rejected the idea entirely.
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.