I am with Selm. I had a baby quilt with a black and white checkerboard sashing. After it was quilted, there were a few dark threads that you could see under the white squares and that annoyed me. But I gifted it anyway and nobody else seemed to notice them. I actually made that same pattern a second time, but was very careful to clip or push any dark frays toward the dark fabric.
I have found that if you insist on cutting exactly on the grain, you get more fraying. I'm just not as particular about that anymore.