Definition: Stay stitching is a single line of stitching, through one layer of fabric, to stabilize the fabric, preventing it from becoming stretched or distorted. Stay stitching is usually called for on the edge of a piece of fabric that has a bias cut to it which would allow the fabric to easily become distorted.
Although it may seem like a step you can eliminate, if pattern directions call for stay stitching, do the stay stitching! It eliminates problems later in having collars, facing and other pieces of the pattern fit together.
The cut edge of the neckline is cut on the bias but the collar is on the straight grain so I will stay stitch the neckline which will allow the collar to fit properly.