Linen is a natural product derived from Flax. Natural linen strops are considered superior for stropping prior to using leather by many straight razor owners.
Strop materials you see that would resemble seat belt materal are not linen and are primarily man made materials. Cotton is also a popular strop material and cotton strops come in different weaves.
And as Martin pointed out stropping incorrectly on any material can damage or dull your blade.