That's sweat and kept damp, not just washing and drying. My work watch strap stank like that. It was worn inside the wrist of my glove and I did six weeks in blazing sunshine one summer, digging/geophys on an enormous double henge on an exposed site.
Nothing I could do got the smell out either.
Get rid of the strap, buy and fit metal or plastic (the sweating is worse, but there's no stink after you take a nail brush and some Fairy to it).
The fabric and velcro Animal straps end up stinking too.
Paracord is a misery; it catches hold of dirt, dust, sweat, salt, it stays dampish and it chafes.
What do folks who work in the jungle type environments use ?
That's a very trim looking strap Toadflax
matches the watch really well.
cheers,
Toddy