People don't normally change thread color. You are free to choose whatever you think will look good to use throughout. Nowadays there are nice variegated threads (multi-color) that can look very nice too.
The only problem with not sewing across the outer blue sashing strip is that then you will be faced with burying the thread ends of your quilting lines or knotting in place. The simplest thing to do is to continue your quilting lines across the sashing so that the ends will be buried in the binding.
Knotting thread ends means sewing in place for 3 or 4 stitches with your machine, which can make a bump that you may or may not find acceptable.
Burying thread ends means doing this by hand. Using a specialized needle that has a hole in the side makes this much faster and easier. Leah Day on her website has a demo video that shows how to do this.