The effect of acids and bases depend on the type of fibre.
Animal fibres like wool and silk are proteins. Peptide bonds are more easily hydrolysed by bases rather than acids and hence these would lose their tensile strength when treated with bases.
Plant fibres like cotton and linen are long chains of polysaccharides and glycosidic bonds are more susceptible to acids than bases.
The tensile strength of synthetic fibres like nylon, polyester remain unaffected by either acids or bases.