Back on the ranch when I was a kid we frequently used rivets for leather harnesses, tack etc. Solid copper rivets are available at any hardware store in various lenghts. You then flatten the rivet over a washer with either a device designed to squeeze the rivet, or with a hammer and anvil.
There are also various hollow rivet designs available in various materials. These tend to use a special punch to roll the material back over on top of the washer to secure the rivet.
One thing I would be sure to do when riveting nylon webbing is to make sure the holes are sealed by punching them with a soldering iron or a heated punch. Otherwise they wil start to unravel from the holes outward. With a rivet in soft material, the rivet needs to be very snug to prevent the material from working under the rivet which will enlarge the hole and eventually cause the riovet to fail.
In my opinion, sewing is stronger than riveting straps together and the relative ease of sewing nylon webbing versus leather makes sewing preferable. But it is also a question fo how strong do you really need it. Rivets will certainly do the job and are more practical if you do not own a sewing machine or have access to a shoe reapir shop, saddle and tack shop, etc.