Arthritis prevents me from pulling a thread or tearing, so I use my ruler & rotary cutter. First, my fabric must be washed and pressed. What I do is hold the selvege edges together at eye level, hands about shoulder-width apart, and look at the bottom (nearly-folded) edge. When this bottom edge lies straight to the eye, I use that as my guide to straighten the edge with rotary cutter/ruler.
If I am off, there will be a "kink" in the cut strip that either looks like a "v" or a "^". If that is the case, I start again.
This works for any fabric, the expensive LQS types, or the cheaper types from a discount store. I never rely on the fold being exactly parallel to the selvege, nor do I rely that the selvege is perpendicular to the crosswise threads. I used this method when I taught quilting, and it has never failed me.