Flag lowering, more than anything else has been a tradition, not reserved just for Americans, but for people in general who did deeds that were deemed positive for America and the world at large in some way, OR if they were great American citizens. The flag has been lowered for the passing Winston Churchill, Gandhi, and John Lennon among other non American citizens.
Though I share your opinion that the seperation between Church and State is all but gone, I view this more of a sign of respect for a figure, not as a religious gesture.