Turley Foot's hemp webbing is pretty good stuff. The thinner ones (as in width) are stiff enough that they won't bunch up on you. I used a wider one, herringbone style, for a cartridge box strap and it works well, but it'll bunch at times. It's all well made.
I considered replacing a leather shot pouch strap with a hemp one, but it has never bunched up on me so I've left it. Just my experience. I think woven hemp looks a lot better, really, and an inch wide one has worked well for a haversack. Note, I replaced the linen haversack strap because it bunched up and dug into my shoulder like a string. It was pretty uncomfortable, and I go pretty light.
Just my experience and preferences after some experimentation. Always found the right combo with this gear to be a balance between utility and appearance.
If you make a leather one and dye it, I'd seal it as well so it doesn't bleed the dye into your clothes. This is especially true if a super hot day.
Enjoy the new gear, whatever you choose!