In my opinion, it doesn't really matter whether you choose to use cotton or acrylic yarn. I've used both for baby items and have never had any problems.
When deciding on a yarn for baby items, I usually make sure to choose a yarn that will be soft and cozy against their skin and that is machine washable ... those are the factors that I consider first, rather than focusing on the fiber content of the yarn.
Hope that helps! I'm sure others will have additional insights for you as well though!