I do very, very little machine embroidery, but I would use a tear-away stabilizer.
You could always hand wash the red fabric. I would personally toss it in the wash unless it was already cut to size, but if you prefer to hand wash it, I would add in a tablespoon of Tide Free to the laundry sink & gently agitate with my hands. Then I would toss it in the dryer on low I just did that with 2.5" strips and they came out perfect -- no frays or shrinkage.