The Weave Engine is a Shader Nodegroup that will create the base fabric texture. This node can achieve a lot of weaving styles based on how you set the parameters. It requires a flat texture coordinate such as UV maps or the X and Y dimensions in the 3D texture coordinates.

Yes, you can download the zip file, extract it and open up the blend file within. Then you can change the colors, the stripe size and thickness, the arrangement of the stripes, the number of threads per repeat, etc. You can easily create a new fabric material to perfectly match your project aesthetic.