The Ben Ish Hai (Rav Yosef Haim of Baghdad, 1839-1933), in Parashat Balak (Halacha 2), discusses the prohibition of Setam Yenam, which forbids partaking of the wine of a non-Jew or wine that was touched by a non-Jew (listen to audio recording for precise citation). If the non-Jew is an idolater, than the wine is forbidden both for drinking and for any other kind of benefit.
However, the Ben Ish Hai writes, if a non-Jewish, pagan child touches the wine, and the child is too young to understand the concept of idolatry of idolatrous worship, then the wine he touches is forbidden only for drinking. Since the child is too young to worship idols with an understanding of what it means, one may derive benefit from the wine he touches. The wine is, however, forbidden for drinking, even if the child is just a newborn infant.
This applies only to children of non-Jewish pagans. In the case of a Moslem infant who touches wine without intending at all to touch it, the wine is permissible even for drinking. Moslems believe in the oneness of God, and are thus not considered idolaters. Therefore, the status of wine that they touch is more lenient than that of wine touched by idolaters. Specifically, wine touched by a Moslem is forbidden only for drinking, but not for other forms of benefit. And additionally, the Ben Ish Hai claims, if a Moslem infant touches wine unintentionally, the wine is permissible even for drinking.
In the next Halacha, the Ben Ish Hai addresses the question of "Safek Setam Yenam" – a product regarding which we are uncertain whether it contains non-Jewish wine, or wine regarding which we are uncertain whether it was touched by a non-Jew. The Ben Ish Hai writes that in cases where we are uncertain whether it is the wine of a Moslem, the wine may be used, even for drinking. He gives an example of a certain kind of honey that Arab merchants would occasionally mix together with wine. The Ben Ish Hai writes that this product may be eaten, noting that Rav Haim Vital (1543-1620) testified to the fact that the Arizal (Rav Yishak Luria of Safed, 1534-1572) partook of this kind of honey. Since it is questionable whether or not the honey contains non-Jewish wine, and the non-Jew in this case in any event is a Moslem, who is not considered an idolater, the honey is permissible.
Summary: If a child of non-Jewish pagans touched wine, the wine is forbidden for drinking, but other forms of benefit are permissible. If the child of non-Jews who believe in a single God – such as Moslems – touches wine, and did not have any intention to touch the wine – as in the case of a young infant – the wine is permissible even for drinking. If a product might contain wine of Moslems, and this is uncertain, the product is permissible for consumption.
