I started embroidering in 1962 when I was 8 years old, I embroidered everything from towels to squares for quilts, pictures to be framed and Christmas stockings. Once in a while the red would bleed - but it would rinse out. All of the items were always hand washed and blocked. And I have embroidered more than my share of pillow cases that were washed in the washing machine without any problem. I have even made baby blankets with embroidered blocks that were washed on a fairly regular basis. So I doubt you will have any problems unless they are very old and the fabric is weak.