Is this vertical crack/split in stud significant?
That crack looks fine to me. From the image it looks to be mostly superficial... I might drill a pilot hole if the screw is going dead center where the crack is, just to make sure the crack doesn't widen. If you want to err on the safe side, you can get another 2x4 stud and nail it to the side of the existing, cracked stud (this is called sistering) with some 10D nails every couple of feet and then attach this item to the new 2x4 stud.