The fact that he does it while on duty is problematic. As a representative of the government (or company, for that matter), he has a responsibility to pursue his ministry outside the bounds of his duties.
It's much the same as if I started using my company's time to evangelize my coworkers (or customers). I'd be shown the door, post haste.
I would have to disagree with you because our Founding fathers put no such restriction in the documents or in practice.
In fact quite the opposite was true. It was not uncommon back then for 2 leaders to share a prayer before getting down to business "For the people".
We have done alot worse since that practice has been effectively abolished.