I prepared my fabrics for sewing by straitening the grain using the technique I was taught years ago during a class I was participating in. I am not sure anyone uses this technique any more, but I have done it for so long I cannot sew without first following these steps.
On the cut edges I clip one end about 1/2 to 1 inch from the edge. This is usually enough to get a strait edge all the way across, but if it is not just repeat the process. I then careful tear the fabric and it will tear easily and strait along that cut edge. (some fabrics will not tear, with these you must pull a thread, very carefully, and then cut along that line the missing thread leaves, if the thread breaks, cut as far as you can then pull some more of the thread).