When you mix cotton and polyester together, you get a fabric that's stronger and more durable than either one alone. The polyester helps to reduce the cotton's tendency to shrink, making it a great choice for clothes that need to be washed and worn frequently. But, it's not a guarantee that the fabric won't shrink at all.
So, will 70 cotton 30 polyester shrink? The answer is, it depends. If you wash it in hot water or dry it on high heat, it's more likely to shrink than if you wash it in cold water and dry it on low heat. But, even if you follow the care instructions to the letter, there's still a small chance that the fabric could shrink a little bit.
Does 70 cotton and 30 polyester shrink? - YouTube