"Why would it be absurd to baptize a Catholic or a Protestant?"
Because it goes against the canons that have consistently held that those who receive Trinitarian baptism are not to be rebaptised but received through profession of faith and/or reconciliatory chrismation. Unless you are going to argue that Catholics and Portestants should be held worse than Arians or Quartodecimans.
First Council of Constantinople
Those who from heresy turn to orthodoxy, and to the portion of those who are being saved, we receive according to the following method and custom: Arians, and Macedonians, and Sabbatians, and Novatians, who call themselves Cathari or Aristori, and Quarto-decimans or Tetradites, and Apollinarians, we receive, upon their giving a written renunciation [of their errors] and anathematize every heresy which is not in accordance with the Holy, Catholic, and Apostolic Church of God. Thereupon, they are first sealed or anointed with the holy oil upon the forehead, eyes, nostrils, mouth, and ears; and when we seal them, we say, "The Seal of the gift of the Holy Ghost." But Eunomians, who are baptized with only one immersion, and Montanists, who are here called Phrygians, and Sabellians, who teach the identity of Father and Son, and do sundry other mischievous things, and [the partisans of] all other heresies-for there are many such here, particularly among those who come from the country of the Galatians:-all these, when they desire to turn to orthodoxy, we receive as heathen. On the first day we make them Christians; on the second, catechumens; on the third, we exorcise them by breathing thrice in their face and ears; and thus we instruct them and oblige them to spend some time in the Church, and to hear the Scriptures; and then we baptize them.
Synod of Trullo
THOSE who from the heretics come over to orthodoxy, and to the number of those who should be saved, we receive according to the following order and custom. Arians, Macedonians, Novatians, who call themselves Cathari, Aristeri, and Testareskaidecatitae, or Tetraditae, and Apollinarians, we receive on their presentation of certificates and on their anathematizing every heresy which does not hold as does the holy Apostolic Church of God: then first of all we anoint them with the holy chrism on their foreheads, eyes, nostrils, mouth and ears; and as we seal them we say--"The seal of the gift of the Holy Ghost."
But concerning the Paulianists it has been determined by the Catholic Church that they shall by all means be rebaptized. The Eunomeans also, who baptize with one immersion; and the Montanists, who here are called Phrygians; and the Sabellians, who consider the Son to be the same as the Father, and are guilty in certain other grave matters, and all the other heresies--for there are many heretics here, especially those who come from the region of the Galatians--all of their number who are desirous of coming to the Orthodox faith, we receive as Gentiles. And on the first day we make them Christians, on the second Catechumens, then on the third day we exorcise them, at the same time also breathing thrice upon their faces and cars; and thus we initiate them, and we make them spend time in church and hear the Scriptures; and then we baptize them.
And the Manichaeans, and Valentinians and Marcionites and all of similar heresies must give certificates and anathematize each his own heresy, and also Nestorius, Eutyches, Dioscorus, Severus, and the other chiefs of such heresies, and those who think with them, and all the aforesaid heresies; and so they become partakers of the holy Communion.
Synod of Laodicea
Persons converted from heresies, that is, of the Novatians, Photinians, and Quartodecimans, whether they were catechumens or communicants among them, shall not be received until they shall have anathematized every heresy, and particularly that in which they were held; and afterwards those who among them were called communicants, having thoroughly learned the symbols of the faith, and having been anointed with the holy chrism, shall so communicate in the holy Mysteries.