The following explanation is for sashings that do not include cornerstones.
Sashings typically need to be cut in both short lengths and long. The short lengths go between the quilt blocks, joining them side to side. Once you have these strips of blocks alternating with short sashing strips, you add a long strip to join two rows.
Strips cut from the WOF (cut on the crossgrain) have slightly more stretch than strips cut from the length of the fabric (lengthwise grain). The lengthwise grain is always the most stable.
For short sashing strips, such as those between the blocks, crossgrain is just fine. For long sashing strips, if you really want more stability and less stretching, then you can cut from the lengthwise grain. This is often inconvenient, and usually unnecessary, but it's fine to do it.
The entire stretching issue can be avoided if you heavily starch your fabric before cutting strips. What I do for yardage is mix a 1:1 solution of Sta-Flo liquid laundry starch and water, "paint" this on the yardage using a large wall painting brush, wait a couple of minutes to allow the solution to penetrate the fibers, toss in the dryer, then iron with steam. This stabilizes the fabric so much that the strips will not stretch as you handle them, no matter which grain they are cut on.