This paper concerns the management of natural waste fibres. The aim of this research was the production of multifunctional acoustic and thermal insulation materials from natural protein and lignocellulosic fibre wastes, according to a circular bioeconomy. For the manufacture of the materials, local mountain sheep wool and a mixture of bast fibre waste generated by string production were used. Insulating materials in the form of mats produced by the needle-punching technique with different fibre contents were obtained. The basic parameters of the mats, i.e., the thickness, surface weight and air permeability were determined. To assess barrier properties, sound absorption and noise reduction coefficients, as well as thermal resistance and thermal conductivity, were measured. It was shown that the mats exhibit barrier properties in terms of thermal and acoustic insulation related to the composition of the mat. It was found that mats with a higher content of the bast fibres possess a greater ability to absorb sounds, while mats with higher wool contents exhibit better thermal insulation properties. The produced mats can serve as a good alternative to commonly used acoustic and thermal insulating materials. The production of the described materials allows for a reduction in the amount of natural fibre waste and achieves the goal of “zero waste” according to the European Green Deal strategy.