So far as I know, the Church takes no position on the matter. Like most things pertaining to behavior during Mass, there is only personal judgment and common sense. Unfortunately, these days, those have been clouded by our society’s idea that personal autonomy and convenience trumps all other considerations.
I can only give you my opinion, and keep in mind that it is an opinion and given only because it was solicited. I believe that children should not be fed at Mass, by any means. If a child needs food, however it is delivered to him, then he should be fed outside Mass. A nursing mother should either feed her baby just before Mass, just after Mass, slip outside with the baby if necessary and possible (or at least move to a secluded area) – or, if none of these options are possible, stay home with the child. (Care of small children is just reason to miss Mass.) While I cannot say so from personal experience, I can say that the nursing of babies in public is a relatively new phenomenon and that there is no evidence from history that babies died of malnutrition by not being nursed in public (either at Mass or elsewhere in the public domain).
Keep in mind also that there is a larger issue here than the feeding of babies. There is also the problem that how you interact with your child at Mass now trains him in how to behave later. As advocates of public lactation like to point out, nursing is not just about feeding a baby. It is also about soothing and bonding. If you model for a baby that those needs can be met during Mass now, you’ll either have to train him out of expecting to have them satisfied at Mass later or you’ll be raising a child who will eventually graduate to needing snacks, sippy cups, and toys to keep him quiet and entertained at Mass.
Again, I ask that you remember that this is personal, solicited opinion. You are very likely to find good Catholics who will strenuously disagree. When evaluating the opinions you receive, one rule of thumb might be to determine which arguments are being made on the basis of personal autonomy and/or convenience, and which are being made on the basis of consideration for others and reverence for the Mass.
