How would the play be different if the setting/staging were changed?

Well, if the setting were changed, then the title would have to go.  It couldn't be called Fences without a fence.

It's got to be in the back yard, where fences go.  Troy and his people have been in the back of things their whole lives.  Troy has worked the back of the garbage truck: he picks up garbage from the back of white people's houses.  Blacks had to sit in the back of restaurants and ride in the backs of buses.

You can't very well call the play anything else.  It can't be staged on a front porch.  That's not where people drink on Friday nights.  That's not where you swing a bat or where you saw wood.  The front yard or porch has no such connotations.  It has no fences, secrets, or social barriers.  It doesn't keep people in or out.

Fences is built around fences--literally.  The fence is always on stage.  Remove it and you have no play.