A host of x-radiation opaque materials are available on the market, from pourable polymers (used to coat the interior of x-ray units at airports) to impregnated fabric & plastic/rubber sheeting. The constituent in these materials which offers the shielding function is usually powdered lead metal, or a lead glass, due to its stability and low cost.
I am not aware of a fabric that thin, which offers substantial x-ray shielding (aside from thin lead metal foil), but I have a brother who is a dentist, & I will ask him.
