In the first place, because "that amount of medieval forgery" is very, very small; and in the second place, because the entire process of textual criticism is devoted to teasing out transmission errors and forgeries, and if there are areas where it is not practical or realistic to restore the original text, any responsible modern editor will highlight that fact.

There are many types of error that can arise in a manuscript tradition, and of them, religiously motivated forgery is about the rarest that there is. Here's a taxonomy of possible reasons for manuscript errors (taken from Reynolds and Wilson, Scribes and Scholars, 3rd ed., 1991, pp. 222-33):

1. scribes having difficulties in reading the handwriting in earlier copies;
2. changes in pronunciation;
3. accidental omission (e.g. skipping a line);
4. accidental addition (e.g. explanatory notes from the margins getting incorporated into the text, or words/letters being repeated);
5. accidental transposition (e.g. swapping two words or two lines);
6. accidental changes to make words look more like other nearby words;
7. accidental errors caused by contemporary thought;
8. deliberate activity by a scribe.

The upshot is that the vast majority of errors are accidental. Scribes -- ancient, mediaeval, and renaissance -- were on the whole a conscientious lot, though certainly subject to human error. More importantly, there was no continent-wide conspiracy in Europe to edit texts a given way. Scribes acted independently of one another, and when they spotted errors in a text they were copying, they very often tried to correct them. This accounts for nearly all errors in category 8, above: most of them are errors caused by a scribe refusing to believe that the text he was copying could be accurate, when in fact it was; or a scribe correctly spotting an error but doing an imperfect job of correcting it.

It'd be going a little far to say that the system was self-correcting, but it was a system that overall consistently aimed at faithful reproduction and restoration. In that kind of ecology of texts it was not realistic for an individual scribe to have much hope of deliberately changing a text for the whole of the rest of the world and for the whole of the rest of time. That "overall" is a key word, of course: given enough time, enough manuscripts, and enough scribes, you do eventually end up with a non-zero rate of intentional changes.

Here's an example where the text was deliberately changed by a Christian scribe because he was thinking Christian, but where it's still possible to recover the original. In Petronius' Satyrica there's one passage where, according to the sole surviving manuscript, a character says

aut ego non me novi, aut non deridebis, licet barbam auream habeas. Sathana tibi irata sit, curabo...

Either I don't know myself, or you won't get the laugh, even if you have a golden beard. I'll make sure Satan is angry at you...

Now, the original text can't have read Sathana "Satan". It must have been Athana, a Doric Greek spelling of the goddess Athena, who had a cult-site on a nearby promontory (the characters in this part of Petronius' novel are Greeks who speak Latin poorly, and this makes it an especially error-ridden text because of its extreme difficulty).

What happened is that a scribe was copying from a manuscript which had the correct reading HABEASATHANA. Notice the absence of punctuation and word breaks. The scribe recognised that there was a problem, but he didn't realise it was a solecism deliberately written by the original author; he thought it was a manuscript error. He was a Christian who knew Latin perfectly well, but didn't know Doric Greek, so he had never heard of "Athana". He inferred -- very reasonably, if you look at it from his point of view -- that the author must have meant "Satan", but another scribe subsequently corrupted the text. So he "corrected" it by adding the extra s.

So the answer to your question is that while Christianising errors could happen, this case, which is minor and where the scribe was trying to act in good faith, is representative of the kinds of errors we find.

It's fantastically rare to find cases where scribes deliberately changed the text in bad faith, or changed it on a larger scale. Josephus is by far the most notorious case, where one of the two passages where Josephus discusses Jesus (JA 18.3.3) was corrupted so that the transmitted text describes him as "the Messiah". Another case is Herodotus 1.199, where some manuscripts leave out his account of sacred prostitution at the temple of Ishtar; though the bowdleriser's limited success in that case only illustrates how unrealistic it was for misbehaving scribes to expect to taint the entire manuscript tradition. Other cases would be cases where scribes copying Christian texts (like the New Testament) were confronted with multiple texts because of transmission errors, and had to choose between them; and sometimes, in that situation, they would choose the most theologically acceptable variant. Josephus JA 18.3.3 is an extremely rare treasure, as one of the very few cases of deliberate forgery where we can't be confident in reconstructing the original text.