Or was totally inappropriate, and a frightening indicator of how the current administration does not believe in separation of church and state. Not to mention that the man was a reprehensible parasite.

I sure am. He's on record as urging Nixon to do a bombing campaign in Vietnam that would kill a million people (Nixon refused), mocked MLK jr., saying that white and black children would NEVER hold hands and walk together, caught on tape mocking Jews with Nixon, helped organize the Religious Right, etc., which ultimately brought us Trump.
He was a manipulative, greedy person who made a personal fortune from pushing religion.

Had he served in a political or military-capacity?

No I am not. Martin Luther Kings, bust is in the capitol. Graham was indeed a special character in American History so I do not really care. Personally, I never gotten bent out of shape over Graham but at that time I hated the Pope. Now I like the new pope and hate Grahams son.
All in all I believe Einstein should be represented in the WH, Science must share the space of greatness and future. Not freaking religion