I, too, would wash anything that is a red or a dark fabric in a mesh bag. I know you are taking a chance with shrinkage; better safe than sorry. If the fabric is really dark or you have a lot of them, I would use more than one color catcher. I have used as many as 4 at a time and found all four to be really dark when the wash finished.
When I was young and had a lot of energy, I made and machine quilted a king-sized quilt in the garage for a Christmas present for my brother. It was freezing cold and I was wearing gloves without the fingers so I could maneuver the quilt under the sewing foot. I finished at 12:15 a.m. on Christmas morning. I washed it so it would be nice a soft and all wrinkly for him to snuggle under. When I took it out of the washing machine, I noticed that the light colored turquoise fabric ran onto the white fabric. Who would have thought that this very light color would run and bleed onto the white fabric? Fortunately, it bled in such a way, it almost looked like the fabric was made that way. I dried it and my brother never noticed the difference. Back then they didn't have color catchers.
I will never forget the comment he made about the quilt after thanking me for it. He said, "Why would you cut all those pieces of fabric apart only to sew them back together again?" After all of these years, there are times when I ask myself the same question when I am having a problem with sewing a block that doesn't come out the dimension it is supposed to be.
By the way, Salad Spinners...Who would of thought? Great idea for the extra one I have in my garage.