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As a priest I've been ruler in a monarchy. A priest has been judge in the same monarchy. I think the only one they're typically excluded from is General.
This changed when referendums replaced the old voting system.I think infils are still excluded from some appointments, but I'd imagine they can also get elected to things. Perhaps you can't become an infil when in government, though.
It makes no since to have a priest as a marshal. I mean Priest can control a army but to control the army on the field does not make any since.
Can priests now be part of an army? Last I bothered to check, they couldn't.