We will first take a look at the “halachic” element and then, perhaps more importantly, try to put things into perspective.
The gemara[1] derives from a pasuk[2] that mentions both the mizbe’ach (altar) and the shulchan (table) the following idea: “At the time of the Beit HaMikdash, a person would bring a sacrifice and be atoned, but now one’s table brings him atonement.” The primary explanation of this statement is that the atonement power of one’s table stems from the mitzva of feeding guests[3] – a practical, not mystical, concept. Nevertheless, there are several (semi-)accepted halachot that are derived from the spiritual concept that “a table is like an altar,” which may reflect another level of the gemara’s teaching with regard to tables upon which people eat.
Several Rishonim[4] learn from this concept that one should cover metal knives that are on the table at the time of Birkat HaMazon during the week, just as metal is kept away from the mizbe’ach; the altar lengthens life, whereas metal (i.e., weapons) shortens it. The Shulchan Aruch[5] cites this practice as the accepted minhag. In a similar vein, the Rama[6] recommends placing salt on the table, just as salt was put on the korbanot brought on the mizbe’ach. The Magen Avraham[7] cites the Sefer Chasidim,[8] who writes that one must not kill insects on a table upon which people eat, just as one would not do so on the mizbe’ach – again because of the comparison between the two. As usual, when the Magen Avraham states an opinion, most Acharonim follow suit.[9] The Aruch HaShulchan[10] extends this protection of the sanctity of the table to refraining from any action that is unseemly. Other Acharonim mention some specific examples, such as not allowing children to walk on top of the table.[11] All indications are that this matter of respect for the table applies at all times, not only during a meal.
It seems apparent that changing a diaper is included in what the Aruch HaShulchan calls unseemly actions that should not be done on a table used for eating,[12] and he would thus forbid it. Actually, most people would refrain from doing so on health and aesthetic grounds, certainly in the presence of guests and soon before a meal.
Nevertheless, I would not suggest saying anything to the new parents, unless you feel that due to your relationship and/or their personalities, they would take your comments in a positive spirit without embarrassment or resentment. While those who cite this halacha use the word assur, it is difficult to view this post-Talmudic “prohibition” as a classical Rabbinic prohibition of the type from which we should try to protect our friends. (It is also unclear if all authorities accept the Aruch HaShulchan’s extension to all unseemly actions, especially those that are natural and unavoidable, like changing diapers.[13])
It is healthy to be melamed z’chut[14] and see a little logic and even some beauty in the couple’s behavior. First, the halachot relating to excrement do not apply, for the most part, to such young babies.[15] Indeed, the smell is also less oppressive (for most) and apparently somewhat less unhygienic. What is more interesting, though, is the attitude of these parents, who, I would guess, are first-time parents. Their days (and some sleep-deprived nights) revolve around that little bundle of joy, and he or she lovingly occupies their thoughts and actions. With such a frame of mind, they probably view taking care of the baby’s needs as being most natural and beautiful, and it has not even dawned on them that others might be taken aback. I would also predict that in a few weeks, they will “land” a little bit and stop this practice, not necessarily due to halachic realization, but due to a return to normalcy, through which they will “know better.” In the meantime, I would excuse their lack of tact and try to focus on the endearing element of this practice.