I boil my choices down to three factors: Load, weather, and activity.
My standard for shooting bags is 2" wide, but I'll go wider for bigger bags and heavier loads. Bag-weight veg tanned leather really stretches when you get it wet under any kind of load at all. Go to a thicker leather though, and if it gets much above 6 oz and hard temper, and it will chafe the heck out of your neck if it rides up over your collar.
Wool in woven straps stretch a lot when wet, too. If your fabric is too thin, it's going to roll up when you're active with a load and turn into a skinny little rope. I go thicker as well as wider for fabric straps that will be packing a load. My hunting pard has a canvas bag with a doubled canvas strap, and it's shown no sign of stretching in a couple of years of fairly heavy loads. We both think the canvas bag is awful noisy for use in the brush, though.
Don't know nuthin about whether it's PC or not, but my favorite is to double layer the 3 oz leather I prefer for bags, then stretch the heck out of it before cutting it to length. I've tried both stitching two layers together (long winter nights) and gluing. Now I prefer cutting the strap twice as wide as needed, applying rubber cement, then folding the two sides in to meet the middle on the back side of the strap. First I did, I was worried about delamination, so I stitched it too. Since then I got smart and tried rubber cement only. Works great and no delam.
