Growing up, I went to a church where we (the choir and kids) processed in carrying the Christian flag and the American flag and singing "Onward Christian Soldiers". Even as a little kid, that totally creeped me out. I would cry and beg my parents to not send me to that church. The front of that church held 3 displays -- Christian flag on the right, Cross in the middle and American flag on the left. As an adult, although I didn't specifically seek it out when I started going back to church, I'm very happy to say that my Presbyterian church displays neither a Christian flag OR an American flag OR a Cross - and in 20 years, I have never heard the hymn "Onward Christian Soldiers" 
It's Colonial era of the Quaker variety - pews, walls, and an elevated pulpit.
The churches I've attended where they have been displayed (especially right next to the Christian flag) are fundamental/evangelical type churches.
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