What thread to hand stitch a binding, and why?
 

I use Rasant which is a cotton wrapped around poly for piecing and binding but I have also used what I have on hand as poly does no damage to cotton fabrics.

I am more likely to colour match than the make of thread. You don't want the stitches to show.

I use 100% cotton thread only, just don't like polyester thread, and cotton-covered poly thread feels like thin wire to me. I usually use the thread that I used for quilting the quilt.
Greetings from foggy Bavaria!

i generally use silk thread for bindings, it is fine/thin; strong, i have a good variety of colors, and it disappears. is wonderful to work with (fine, no lint, strong) i can make really tiny stitches with it- i just love to work with silk threads and use them for most of my hand work, appliques, english paper piecing, and bindings.
if i don't have the correct color i will generally turn to a good polyester or aurafil for bindings- cotton thread is just not strong enough (in my opinion) i've had to replace way too many bindings for people where the cotton thread simply gave away with time/use/laundering...i prefer threads that are strong-will last the test of time.
i do use cotton thread for machine piecing often- knowing that the quilting process will help add stability & strength to the finished project

I usually use poly because it is strong.

On the one I'm working on now I'm using rayon. It just happened to be the thread that best matched. I blanket stitch so it does show some. I like it that way.

I never actually thought about it. I try to match it to the color of the binding fabric.

I use whatever I have that's reasonably strong and the right color. Usually Dual Duty Plus -- leftovers from years of garment and home dec sewing. I don't like most all-poly threads. I find that the all-cotton "hand quilting" threads are usually a bit stiffer than I want for binding.

I guess I never thought much about what kind of thread to use. I just pick whatever is a reasonably close color match that I have on hand. Usually it is the same as I've used for piecing and/or quilting.