I know what the OP is talking about and I've taken those types of bags before as well to hold dirty clothing in transit. I'm not exactly sure that they're cloth in the traditional sense - it's a very loosely formed, almost paper-like material, with the Conrad lettering screen-printed on it. OP isn't talking about sewn, embroidered cotton laundry valet bags like you see at a Ritz, etc.

The only point of comparison I can think of for the material is that it's similar to what's used on the underside of furniture, and the closest I can find with moderate searching would be at this link - https://www.fabricfarms.com/UP110.html

To the OP's original point, if you've ever accidentally washed a Kleenex, that is what I picture happening to one of these in a washing machine. But anything is worth a try once to find out!

And on the sustainability topic, I've had two carefully-selected "disposable" plastic laundry bags from higher-end hotels/stores that I've been using weekly for my dirty travel laundry now for over a year. I think it's a happy medium - pretty low impact across the board.