I always tear backing to be sure I have a straight edge to start with.
I learned to quilt from my Grandma when you traced cardboard templates with a pencil, cut each patch with scissors and hand sewed each patch. She always tore her fabric before starting to trace so her patches would be even, she used the torn edge as her guide for tracing. I have several for her quilts that are 70-80 yrs. old. I'm still using them and the torn edge doesn't seem to have effected the endurance of the quilt at all.