Given that it cuts really quickly and cleanly, it's a relatively rare request. But it does come up, mostly felt for jewellery.
Man made fabrics will cut with a clean edge and perhaps a slightly plasticky smell, which will dissipate over a few hours
Natural fibre based fabrics will cut, but any smell and the quality of the cut edge will vary. If you're concerned about how a material will laser cut, just try setting fire to it! But seriously, send us a sample if we've not already tried cutting it and we'll be happy to try cutting it.