There is some dispute on this issue among the Orthodox, but my own position, which has the support of several prominent authorities, is that the guilt of “original sin” is not inherited: every newborn is innocent.

I would cite, for example, The Orthodox Church, by Metropolitan Kallistos (Ware), in which the author points out that the “Orthodox have never held (as Augustine and many others in the West have done) that unbaptized babies, because tainted with original guilt, are consigned by a just God to the everlasting flames of Hell”. The reason for this difference, Ware explains, is that in the Orthodox perspective, men “inherit Adam’s corruption and mortality, but not his guilt: they are only guilty in so far as by their own free choice they imitate Adam.” Now it is true, he continues, “that an Augustinian view of the fall is found from time to time in Orthodox theological literature”—perhaps it is some such exception you have in mind—but this, His Grace observes, has been the result of western influence (see The Orthodox Church [Penguin, 1991], p. 229).

Agreeing for the sake of the argument that the Orthodox point of view may be correct, you say you’re nonetheless puzzled, as a Catholic, why infants should in this case be given the initiatic Mysteries. Are these not “irrelevant” or “superfluous”? Here in answer I would quote from another noted Orthodox theological authority, John Meyendorff:

“The Church baptizes children,” writes Meyendorff, “not to ‘remit’ their yet non-existent sins, but in order to give them a new and immortal life, which their mortal parents are unable to communicate to them.” This is the aim, in fact, of all the Mysteries: “Communion in the risen body of Christ; participation in divine life; sanctification through the energy of God, which penetrates true humanity and restores it to its ‘natural’ state, rather than justification, or remission of inherited guilt—these are at the center of Byzantine understanding of the Christian Gospel” (Byzantine Theology [Fordham University Press, 1974], p. 146).