I recently got a question on my review of the Tulip tie-dye kit as to why everyone recommends 100% cotton items for tie-dyeing.
The reason for the 100% rule (down to 80% cotton usually works fine too) is that polyester fibers are, when you get right down to it, plastic. Think about the polyester fleece now made from recycled soda bottles (such as that in Patagonia products), and you have the idea. The Procion dyes used in the Tulip kits (as well as Dharma and Jaquard) wash right off of plastic (gloves, table covers, etc.). So that's what happens with your shirts. If you look closely at the cotton/poly, you should be able to see white fibers after washing the excess dye out. That's the polyester.
Here are some examples. The following picture shows a rag I use to clean up my dye spills (thus the mottled colors). It's a piece of thermal underwear that is a cotton/poly blend.
Here is a closeup of the same piece. The white threads are the polyester. The cotton has taken the dye.
It's almost impossible to find pure cotton socks, since synthetics such as polyester and nylon help the socks wear much better. Also, any elastic used in the socks will be non-cotton itself and probably covered in polyester or nylon. The trick is to find socks that hide the polyester or other synthetics as well as possible. Usually you will have to try dyeing a pair to see how they work, since it's impossible to tell the difference when the socks are still white.
This sock shows a lot of synthetic content in the foot, but less in the folded-down cuff. If you like the heathery mismatched look, it's fine.
This sock dyes quite well. The foot is only a little heathery, and the outside of the slouch cuff hardly shows white at all.
Here is the closeup. Note that the elastic around the cuff is fairly well hidden on the inside. You can see the white flecks in the foot area.
Here are two turtlenecks I dyed. The one on the left is 100% cotton, and the one on the right is 60%cotton/40%polyester. The turquoise and navy shades are supposed to be the same in both shirts.
You can't quite see the white threads here because they are so fine and well interspersed with the cotton, but it's definitely the polyester making this shirt so faded looking.
This is where the turtleneck attaches to the poly-blend shirt. The turtleneck is a somewhat different blend from the shirt body, and it contains 10% spandex. It is also a different weight and knit from the body. Note that the two different blues are the different fabrics' reaction to the same dye color. There is no way I could have intentionally dyed these different shades with such a clean line between them!
The following is the 100% cotton shirt. Note that in both this and the previous shirts, the stitching is pure white. It's polyester. For most shirts, nobody would notice, or if they did, they would think that it's intentional contrast stitching. However, this is why Dharma notes on almost all of their garment blanks whether they are stitched with polyester thread (they often say "Not cotton thread"). For some garments, visible white stitching would be an unwelcome surprise.
Dyeing polyester requires different types of colorants, since most fabric dyes just wash off the fiber. Dharma offers one type of dye for polyester but it requires hot water, and it usually needs to be simmered on the stove. Since I'm more of a natural fiber fan, and I'm too lazy to use anything other than the cold-water Procion dyes, I haven't tried it myself.
Respect the Blends
Keep in mind that you can get interesting effects using the cotton/poly blend fabrics, such as the patterned effect on the thermal underwear knit. I've seen tops in stores recently where the fabric is knit in stripes or patterns of cotton followed by polyester blend, providing a very cool arrangement of strong and pale colors. Also, if you like pale pastels, blended fabrics give you an easy way to do it.