I also never hold my fabric up to square it. I start from the factory fold and cut perpendicular to that. If I need to fold again, I fold that factory fold and simply make sure that the measurement between the folds is the same all across the fabric.
What is important in terms of getting straight cuts on strips is that the ruler be exactly perpendicular (90 degrees) to the fold. You can test this with a piece of paper, pretending it is fabric. Fold any way you want. When you cut exactly 90 degrees from that fold, the strip will be straight when unfolded. The more you deviate from 90 degrees, the more of a "bend" there will be in the strip where the fold was.