I've never heard this before! We have a breadmaker and make all our bready stuff in it, and did so while I was breastfeeding.
Beatrice has been having bread sticks since she was about 6 or 7 months with no ill effect.
Top tip, by the way: if you add a spoonful of yeast extract (marmite/vegemite/whatever brand) to the mixture, it makes really tasty bread sticks. When the loaf is a day or so old, cut a slice into soldiers and microwave for about two minutes or so. Allow them to cool down and they'll be quite hard - great for little ones to chew on, and cheaper than commercial rusks.