Yeah, the states had constitutions promoting a religion, even after the US Constitution was ratified. Of course, things have changed, but I think you are right.
As a kid I was taught that when visiting a church of different faith from my own to sit in the back watch and if I cared to join in to do so.
If not then to sit quietly respectfully and when service is over to shake the hand of the Celebrant and thank them.
So whats so hard about that, if a meeting were to be held in a church that handles snakes, I may leave early or not depends on just how wild it gets.
At a business meeting, I have no problem with saying thank you for the food we are about to eat in any religion.
At work when I see someone bow their head and mumble a thanks to what ever God they are thanking, I cannot help but smile and feel that these people are trustworthy, grateful and good folks.