Many bubs who are dairy intolerant or also soy intolerant. I don;t know the percentage off hand but something like 50%. So the advice is to go soy free if you are going dariy free as a precaution.
See this website for more info:
http://mspikids.info/ I had been dairy/soy/gluten free since Ds2 was 3 weeks old (now 5 months) and still getting green mucus poos. I looked into it and basically anything thatis labelled as an allergy food or an intolerant food can cause the mucus poos, it means their digestive tract and bowel is irritated and damaged.
Don't know anything about the milk you mentioned.
Anyway, I cut egg, an still problems. Then I went on the Royal Prince Alfred Allergy Unit Elimination Diet which also moderate in natural food chemicals such as amines, salicylates, and glutamates and no preservatives or additives. I also went as dairy/soy/gluten/egg free, and still mucus poos but ALOT less in frequency and all his symptoms are minor but we are still getting them.... so basically now its down to the fact that I am on the "moderate" diet and not the "low" diet, he can't even tolerate low amounts of these food chemicals it seems.