My baby has mucusy runny like poop, she is one month old. could this mean a milk/soy reaction?

Depends: Is she exclusively breastfeeding or on a cow's milk or soy based formula? If she is growing, developing and doing well with her well child care visits there should be no concerns regarding her stool characteristics. If she is not gaining weight and having other developmental issues-see your pediatrician for guidance.

Yes: Mucous in stools suggests irritation of the lining of the intestines. One reason for this a tthis age would be allergy. The most likely culprits, if allergy, would be milk and/or egg but soy is possible as well. If breast feeding try a 2 week period off milk products and see what happens, if not better try this with egg, finally soy. If better probably was an allergy and should be outgrown later.