Nylon isn't hard enough to scratch steel... This is completely avoidable by simply washing your NATO straps every couple days. The strap is collecting all of your dead skin cells, sweat, salt water, sand, dirt and other debris. Sweat/salt in particular can be very hard on steel. All of those things combined rubbing against the caseback of you watch is the issue.
Here's a photo of my Speedmaster and some of our well-worn straps. This Speedy has lived on various NATOs for years as I prefer them to the bracelet. You can see there are no scratches from the straps, I just swap straps every couple days and wash the one that I've been wearing.
The only real wear on the caseback is from wearing the watch on a bracelet - my wrist/sweat has rubbed off some of the paint or the bracelet has rubbed against the caseback when setting the watch down.
Just wash your straps regularly and enjoy them.
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