As Harry Gamble explains, the early heretical opponents of Christianity had the New Testament text in common with the orthodox mainstream. Rather than accuse the mainstream of significantly altering the text, they seem to have accepted the text and attempted to get around it by means of a less literal form of interpretation:
"This means that what was at stake between gnostic and non-gnostic Christians was not principally which books were authoritative, but rather how the scriptures were to be rightly interpreted. In point of fact, gnostic Christians employed virtually all the books that were used in the church at large. The difference lay not in the documents, but in different hermeneutical programs." (Lee McDonald and James Sanders, edd., The Canon Debate [Peabody, Massachusetts: Hendrickson Publishers, 2002], p. 293)
Trypho, a Jewish opponent of Justin Martyr, comments that he's read one or more of the gospels (Dialogue With Trypho, 10). And Justin cites the gospels and alludes to other New Testament documents frequently in his dispute with Trypho. Justin makes much of alleged Jewish corruption of some portions of the Old Testament text (Dialogue With Trypho, 71-73, 120), yet both he and Trypho seem to assume a common text for the New Testament. (There would have been some textual variants, of course, but they apparently weren't of much significance.) Why would Justin have put such emphasis on Old Testament corruption if he thought that significant corruption of the New Testament was a common Christian practice? Why is there no need for him to interact with any such charge from his Jewish opponents?
Some early opponents of Christianity did make the charge of textual corruption, but it seems to have been a minor charge that didn't come up very often. Celsus, a second-century Gentile critic of Christianity who got some of his information on the religion from Jewish sources, wrote:
"Certain of the Christian believers, like persons who in a fit of drunkenness lay violent hands upon themselves, have corrupted the Gospel from its original integrity, to a threefold, and fourfold, and many-fold degree, and have remodelled it, so that they might be able to answer objections." (cited in Origen, Against Celsus, 2:27)
Notice that Celsus cites no evidence for the claim. And he only brings the charge against some Christians, not all. He doesn't even claim that it's a majority. Celsus often exaggerated. On the subject of unity, for instance, he wrote:
"Christians at first were few in number, and held the same opinions; but when they grew to be a great multitude, they were divided and separated, each wishing to have his own individual party: for this was their object from the beginning....being thus separated through their numbers, they confute one another, still having, so to speak, one name in common, if indeed they still retain it. And this is the only thing which they are yet ashamed to abandon, while other matters are determined in different ways by the various sects." (cited in Origen, Against Celsus, 3:10, 3:12)
He's speaking hyperbolically. But when this critic of Christianity who often exaggerated was addressing the New Testament text, he only referred to what "certain of the Christian believers" did.
As you read through Origen's entire treatise Against Celsus, it seems that the two men argue on the basis of the same text, aside from relatively minor variants. If Celsus had much knowledge of some significantly different earlier text, one wonders why he didn't make more use of it.
Origen's response to Celsus assumes that Celsus was addressing textual corruption, but some scholars think that he may not have even been discussing the subject (Henry Chadwick, ed., Origen: Contra Celsum [New York, New York: Cambridge University Press, 2003], n. 2 on p. 90). Instead, he may have been referring to the existence of multiple gospels among Christians (Matthew, Mark, Luke, John, and others among some professing Christians). If so, then Celsus' charge isn't even relevant.
But Origen possessed a copy of Celsus' treatise, which we don't have, and his reading of Celsus seems preferable. Origen was in a good position to comment on the text of the New Testament. He traveled widely, he was in contact with many Christian and non-Christian sources, and his life reflects well on his character. He responded to Celsus:
"Now I know of no others who have altered the Gospel, save the followers of Marcion, and those of Valentinus, and, I think, also those of Lucian. But such an allegation is no charge against the Christian system, but against those who dared so to trifle with the Gospels. And as it is no ground of accusation against philosophy, that there exist Sophists, or Epicureans, or Peripatetics, or any others, whoever they may be, who hold false opinions; so neither is it against genuine Christianity that there are some who corrupt the Gospel histories, and who introduce heresies opposed to the meaning of the doctrine of Jesus." (Against Celsus, 2:27)
Celsus doesn't say much about the subject, and Origen doesn't spend much time on it. He doesn't seem to be aware of any significant need to defend the general reliability of the transmission of the text.
Celsus' charge doesn't carry much significance, and Origen confirms what we saw in earlier sources like Irenaeus, Dionysius of Corinth, and Justin Martyr. Altering of texts was considered shameful, and steps were taken to avoid it and to condemn those who practiced it.