What are the arguments against using manuscripts from the Cairo Geniza? Are there any Seforim / articles that discuss this debate?
There was an article in Tradition journal which discussed some of the arguments for and against using manuscripts in Halakha (which is what I'm assuming the questioner is looking for). It is linked here, but I'll summarize some of the main sources that would be relevant to dealing with this question (
especially since the article is behind a paywall even though it can now be accessed for free!).
First off, the question of archeology's relevance to halakha might be applicable here (the closest question on this site is that of science's relevance to halakha, but none of the answers quote the following sources). The basic sources on that topic is the Beis Yosef (O.C. 34) who brings evidence to the fact that the order of parshiyos in the tefillin should be like Rashi/Rambam because very old tefillin were found in the grave of Yechezkel with that order. The Drisha, however, says that it's no proof because it could be that they were written incorrectly and therefore buried in a grave. This also has relevance to the question of using the murex snail for dying tekheles.
A letter from R. Sheraira Gaon discussing textual variants in the Talmud says that multiple texts should be upheld and reconciled - each represents a valid tradition. (It could be argued, though, that newly found texts carry no such tradition)
It is well known that the Rishonim spent much effort to determine the most accurate text of the Gemara. One poignant example is where the Rambam spends some time in his Mishna Torah (Hil. Malveh VeLoveh 15:2) detailing how he procured a very old manuscript of the Talmud and, based on it's version, overturned a previously accepted ruling of the Geonim.
In the Urim Vetumim of R. Yonasan Eibschutz (Klalei Tokafo Cohen 123-124), he states that a litigant/defendant in beis din cannot say 'kim li' like an opinion that was newly discovered from a manuscript, if this opinion runs contrary to that of the Shulchan Aruch. R. Moshe Shternbach (4:274) extends this to any well accepted book of halakha, not just the Shulchan Aruch, meaning that manuscripts are effectively meaningless except in rare cases where there was not yet a generally accepted ruling.
On the other hand, Mishkenos Yaakov (O.C. 120), in discussing a certain ruling of the Rama, lists several Rishonim to whom the Rama did not have access to their works, and states that had the Rama been privy to these manuscripts, he would have reversed his ruling. Therefore, the Mishkenos Yaakov argues on the Rama based on recently 'found' opinions.
While the position of the Mishkenos Yaakov is followed by the Aruch Hashulchan (O.C. 345:17), the Teshuvos Beis Efraim (O.C. 26-27) argues based on the aforementioned Urim VeTumim. Shulchan Aruch Harav, in his siddur, says that one should be strict regarding the sale of chametz because of new manuscripts of the Rishonim that have come to light that wouldn't have been considered by the earlier Achronim. Also on the side of using manuscripts we have R. Yaakov Ettlinger, (Shu"t Binyan Zion 69), who bases a ruling upon a newly discovered version of a Geonic teshuva. This also appears to be the opinion of the Mishna Berurah, as he approvingly cites the newly published Rabbeinu Chananel on Shabbos and uses it to argue upon the version cited by the Ran (Siman 340, Biur Halacha 'bein beyad'). It should be noted, however, that in almost all of the above cases, manuscript evidence was used to rule strictly, not leniently.
The Chazon Ish (Letters vol. III no. 48) says that because the Shulchan Aruch was not actually based solely on the majority rule between the Rambam, Rif, and Rosh (despite its author's introduction), we can't use manuscripts to argue on the Shulchan Aruch, which was accepted anyway. Furthermore, he implies (Eiruvin 67:12) that we shouldn't rely on the newly published Rabbeinu Chananel because, as it hasn't been in use for centuries could therefore contain serious typographical errors. (This observation is also noted by the Seridei Eish in several places as well). In Letters of the Chazon Ish (vol. I no. 32) he also seems angry that someone should try to answer a question in the Gemara based on textual variations, and in vol. 3. letter 2, he clarifies that this is because the accepted version of the Gemara is due to divine providence.
Similarly, R. Moshe Feinstein would dismiss newly discovered writings that ran contrary to his opinion (see Iggeros Moshe E.H. vol. 1 63:6, Y.D. II:7 and Y.D. III:14, plus more).
A further issue is where a manuscript was discovered from an author who isn't known to us as a talmid chacham. R. Ben Zion Uziel writes (Choshen Mishpat, Tinyana 6:2) that we follow Rishonim because of their personal greatness, not the era in which they happened to have lived, and so just because a work is old doesn't make it reliable.
Aside from one or two extra sources, all of this came from the article linked above: Moshe Bliech, "The Role of Manuscripts in Halakhic Decision Making: Hazon Ish, his Predecessors and Contemporaries", Tradition 27:2 (Winter 1993)
There is a similar question relating to the writings of Rabbi Menachem Meiri and would seem to be equally applicable to the question of the Cairo Geniza: Quoting wikipedia:
His commentary was largely unknown for centuries until being republished in modern times. Thus, it has had much less influence on subsequent halachic development than would have been expected given its stature. Some modern poskim even refuse to take its arguments into consideration, on the grounds that a work so long unknown has ceased to be part of the process of halachic development. This is despite the respect they nevertheless have for the commentary and for its author.
I just ran across some additional sources regarding this issue in a comment on the Rationalist Judaism blog ( quoting ):
Both R. Aharon Feldman(about Michtav Meliyahu) and R. Elyashiv conceded that there exist "non-Yeshivish" sources that could be found in the Cairo Genizah, if not elsewhere:
R. Aharon Feldman wrote about the approach considered kefirah, "This approach is mentioned by many eminent authorities in Jewish history...Rabbi Aryeh Carmel, citing an informal conversation with Rav Dessler, in a footnote to Michtav MeEliahu IV p. 355 that the Sages never erred in the final halacha, although they may have erred in the reason they gave for it."
R. Eidensohn wrote about his writing his “Daas Torah” book:
"I then went to Rav Eliashiv - he told me simply that there is no problem of raising issues and presenting multiple alternatives - as long as the source material was from mainstream accepted views. He did not see a problem "as long as I did not present sources from the Cairo Geniza." In regards to the issue of confusion - he said simply "let them ask their rebbes and rosh yeshiva." You don't avoid teaching Torah because it raises questions."
("Questions I - what? vs why? vs silence?" , Daas Torah Blog, 12/4/08)