I do enjoy visiting Anglican churches. Not that I am Anglican myself, but I do appreciate the art and architecture.
One certainly feels different visiting a church as opposed to visiting a museum. One feels that, despite being a tourist, one must behave with a degree of reverance.
I do feel strange keeping my shoes on in a building that is considered sacred; defiling it with my shoes that may have been anywhere. And I am a western Christian who is used to wearing shoes in churches. It must be very weird for a person from an Hindu, Muslim or Buddhist background to visit a Christian church where shoes stay on.
To me it seemed far more appropriate and reverant in Japan where shoes were removed on entering churches.