History of Striped Locomotive Engineers Caps???? - Trains Magazine

The stripped material is pillow ticking...the material pillows were made out of, a light canvas weave, to keep the down or feather stuffing from sticking through the pillows...bed mattresses and furniture cushions were also made from the same, then covered in a more decorative cloth.

I would imagine the material was used simply because it was cheap and readily available, very durable and that most of the early engineers had their wives make them hats out of it to keep the ash and cinder out of their hair.