I always pin perpendicular to the stitching line and sew over the pins. (Cue rancorous sew-over-pins religious war here! 😆 ) I do that for several reasons. When several layers of fabrics are pinned, they are shifted in relationship to each other, like this:
At places where the pin enters and exits the fabric layers, the layers are shifted, the thicker the fabric, the greater the shift. Thus shifted, the fabric layers will be distorted when stitched.
Additionally, if I pin parallel to the stitching line, I’d need to either remove the pins as I sew which I find time consuming, or to pin a distance away from the stitching line, which compromises accuracy.
If I pin perpendicularly to the stitching line, the fabric is still distorted, but in a direction perpendicular the stitching line and thus won’t result in distortion of the stitched seam.
Additionally, I can sew over the pins. (After stitching, I remove pins all at the same time, saving a lot of time.) I know that many people who warn against sewing over pins, citing the danger of hitting a pin and breaking needle, throwing machine out of alignment, eye injury, etc. There is definitely that danger. However, the risk of hitting a pin, and of whether or not the needle will break on hitting a pin, depends on the size of the pins used. I use Clover’s Patchwork Pins which are only 0.4mm in diameter i.e. very very fine. They are flexible and bend very easily but can be bent back into shape, yet they are sturdy enough to anchor layers of fabric. As such, in the very rare times when the needle hits a pin squarely, the pin gets bent, but that’s all.
In the same spirit, when I pin zippers, I pin perpendicular to the teeth and tape as well. Since the pins will “ride” over the zipper teeth and might foul the presser foot, as the second and third pins in the following pic show:
As such, I need to remove the pins rather than sew over them. However, removing the pins negates the point of pinning (to ensure layers do not shift), so instead of removing a pin altogether when I sew up to it, I would pull it out just enough so that only its tip is still engaged, as is the case with the top pin in the above pic. (In fact, I just realized that in the pic, even though the point of the point of the pin is still engaged in the zipper tape, it’s barely visible!) This affords me the benefit of layers still being secured against shifting, yet the point of the pin does not present an obstacle.