The instructor in the class I took earlier this year said today's fabrics are straight enough to not worry about it, but I've found differently. Out of a hundred or so pieces of fabric I've bought in the past six months, only ONE of them was cut on the grain!
I've found that even the very best quilt shop fabrics are not cut on the straight of the grain, so EVERY piece I buy goes directly into the washer and dryer before I do anything else. EVERY piece! Some are off as much as a couple of inches, while others are off by fractions, but still...they are ALL off.
AND, what IF you don't wash and dry them and they shrink after your quilt is all beautifully done if you haven't heavily quilted it? I shudder to think of what the outcome would be and I don't want my quilts to look puckered up after all that work.