I'm not sure I'm understanding the question/concern so here goes. You want your binding strips right sides together when you put them together - same as when piecing blocks. Is your fabric actually 'textured' or is it directional? In my mind, textured has no bearing as long as you've put right sides together when sewing your strips together it should not matter. If it's directional then that may make a difference but usually not so much with such a thin binding strip.
After you've sewn your strips together to get enough length to go completely around the quilt along with about 12-15" extra (for matching/joining ends), you'll fold your entire binding strip wrong sides together and sew it to either the front or back of the quilt (I usually machine sew down to the front of the quilt and then fold over to the back). Some folks press their binding strip in half before stitching down to the quilt but I've found that particular step unnecessary).
After attaching by machine and joining my binding ends together, I then trim the quilt sandwich, fold the binding strip over to the back and stitch down by hand.
Hopefully this answers your question. Good luck.