As Mindless said, a quilt is only as old as it's newest piece.
If it is for you, then finish it however you want. One of the ladies in my group is working on re-piecing some blocks which she feels is post civil war to 1900 fabrics. The original backing was badly stained and couldn't be salvaged. She is using a modern muslin. It is a hand project for her and not a restoration, and that's just fine.
I've been trying to determine the setting, there are definitely blocks with 4 red corners, and the other blocks vary quite a bit. I think it's just funky and not deliberate. It might have never been finished because of that.