When a droplet impacts a fabric mesh at a sufficiently high impact velocity, it not only spreads over the fabric but also penetrates its pores. To determine the influence of this liquid penetration of the fabric on droplet spreading on thin fabric meshes, we measured the droplet spreading ratio on fabric with and without an underlying substrate using a high-speed camera. For fabrics without a substrate, the droplet spreading ratio is reduced as the fabric penetration by the liquid reduces the droplet volume spreading on top of the fabric. Using entropic lattice Boltzmann simulations, we find that the lower droplet spreading ratio on fabrics, both with and without a substrate, is due to an increase in viscous losses inside the droplet during spreading. Comparing droplet impact of blood with its Newtonian counterpart, we show that for spreading on fabrics, just like on smooth surfaces, blood can be approximated as a Newtonian fluid.