I am happy when my FQs don't have selvedges, that means a little more fabric to use and not have to trim away! I, too, am not concerned if my fabric is a little off grain when I am cutting a piece or two. Perhaps being a scrapper is partly why. Sometimes you just have to get that bit where you can. I do NOT do anything to distort the grain, tho, I just use it as is, so there is no reason for it to "change" when it gets washed.
The only time I am concerned about having the fabric grain is when folding and cutting the strips for borders, binding, strip piecing, etc.