Your question about diapered children in shul during tefilla involves two possible issues: 1) Preserving the honor of a beit knesset,[1] which might apply even when it is not the time of tefilla. 2) Davening in the presence of excrement,[2] which is problematic outside of shul as well. (Although the main classical sources discuss Kri’at Shema,[3] the halachot are relevant to davening, making berachot, and speaking divrei Torah.[4]) Your question involves both issues, but we do not believe that the combination of the two is more problematic than the elements separately.
We will first discuss the matter of the honor of a shul. Realize that if it were actually forbidden to bring a baby in a diaper into a shul, a toddler sibling of a baby having a brit in shul could not attend, and this is a stringency we have not heard of. In fact, we have found no indication that bringing a baby in a diaper is considered a disgrace to a beit knesset, and we have no reason to question the clear minhag to allow it.
Turning our attention to the second problem, the presence of excrement has the potential to greatly limit involvement in matters of kedusha in a house in which there are non-toilet-trained children. (Notably, the excrement of newborns during their first several months is not an issue.[5])
An important rule is that the problem of excrement is solved if it is covered.[6] Thus, at first glance, a diaper should be sufficient to solve the problem. However, there are some complications. First of all, there must be no smell (the extent of which is hard to quantify) that escapes the covering,[7] and the smell of excrement affects the area up to four amot[8] beyond the furthest point it reaches.[9] However, poskim rule that one does not have to constantly check to see whether there has been a bowel movement and a spreading smell.[10] If one knows that the baby has eliminated,[11] and perhaps if sufficient time has passed to assume a baby has done so,[12] he should check for a smell.
Moreover, according to the concept of graf shel re’i, a utensil that is used for collecting excrement is considered soiled, and one is not allowed to daven when it is in his view or, if it is behind him or sufficiently to the side, within his four amot.[13] Is a diaper a graf shel re’i, given that it is made to be a receptacle for holding excrement? Rav Moshe Feinstein[14] rules that cloth diapers are not graf shel re’i once they are washed, implying that they are while they are soiled. Therefore, there is logic to require that a soiled diaper be covered (e.g., by the child’s clothes), even if it does not smell.[15]
On the other hand, modern disposable diapers might not have this status, because they are made to be used on an ongoing basis for excrement but are thrown out soon after becoming soiled. Some poskim point out that modern diapers have another advantage – they have their own nonabsorbent plastic covering.[16] Rav S.Z. Auerbach reportedly did not accept this distinction, however, because the covering of graf shel re’i must be something external; the outside of the diaper cannot be considered a covering for the diaper itself.[17] It is not clear what Rav Auerbach’s full opinion was on this matter.[18] In any case, his stringency is applicable only when the diaper is soiled, not if it is just wet.[19]
There is also an opinion that a covering is insufficient if the excrement is located at the anus.[20] However, the great majority of poskim say that the stringency of excrement at that spot affects only the soiled individual, not those davening in his presence.[21]
We conclude that the prevalent practice to allow matters of holiness to be spoken in the presence of a baby in a diaper is very well-grounded. It is laudable to check the diaper from time to time and to change it when the baby is dirty. If one wants to be more machmir than that, he should consider the price. However, he certainly should not impose his view on his fellow congregants.