I do strive to cut on grain. When the fabric is off grain it can stretch. The stretching really shows up at the quilting stage for a longarmer. There will be "valleys and hills" within the blocks. Also, the fabric will not lay down while being quilted which causes pleats and tucks.
Also, if you have a block with bias cuts in the block, if the sashing is off grain that block can really stretch when on the frame.
Just my opinion.