When I first learned to sew, I followed the teacher's directions and pinned perpendicular to the seam line. (And sewed over the pin-I'm still a rebel.)
Then came THE SERGER! Yep! Ran right into the sucker! The pin flew in bits all over the place, really scared me. Put a damper on my using the serger until I had it cleaned, retimed and the cutter replaced.
Not wanting to repeat the error. I started putting pins parrallel to the seam, to the left, so they didn't need to be removed.
Eventually I realized it's the seam that needs to match, not the edge of the fabric. So now I pin baste the seam line. When the machine gets close to a pin, I hold the head with my finger nail and let the machine pull the fabric off of the pin. This way, I don't have to stop the machine to pull out those perpendicular pins.
So, my vote is parrallel.