As noted in this answer, even a sefer torah, if written by a heretic, does not have holy status and needn't be buried. Further, Rambam (Laws of Tefilin, Mezuzah, and Sefer Torah 1:13) writes:
יג ספר תורה תפילין ומזוזות שכתבן מין, יישרפו. כתבן גוי, או ישראל משומד, או מוסר, או עבד, או אישה, או קטן--הרי אלו פסולין וייגנזו: שנאמר "וקשרתם . . . וכתבתם" (דברים ו,ח-ט; דברים יא,יח-כ)--כל שמוזהר על הקשירה ומאמין בה, הוא שכותב. נמצאו ביד מין ואין ידוע מי כתבן, ייגנזו; נמצאו ביד גוי, כשרים. ואין לוקחין ספרים תפילין ומזוזות מן הגויים ביתר על דמיהן, שלא להרגיל אותם לגונבם ולגוזלם.
A Torah scroll, Tefillin, or Mezuzah written by a heretic -- burn it!... If you find one in the possession of a heretic and don't know who wrote it, bury it; if in the possession of a non-Jew, assume it's kosher.
If we destroy even a sefer torah if written by a heretic, then it seems reasonable that at the very least we needn't bury lesser works using the divine name if written by a heretic (min, in the Rambam passage). Are there further rules about what to do with it?
If the book is written by a min we are to burn it. According to the talmud in various places, minim include those who deny God's unity or believe in an independent, divine evil being. Both of those are core tenets of Christianity. A book produced by Christians for missionary purposes seems to qualify the producer as a min, as argued in the answer I linked.
This blog post provides further support:
I met with Rabbi Riskin last week (it was a good meeting), and he mentioned that several years ago the residents of Efrat received missionary bibles in the mail - as part of a campaign to convert Jews - and he poskened that people should burn them ( the missionary materials, not the missionaries).
The author of that post later reported:
The ruling was to burn the entire bible which included both the Hebrew and New Testament Bible. A Bible which is written on a heretical basis is not considered sacred. However, at the time I did not think to ask how Rabbi Riskin felt about burning the new testament exclusively or the exclusive new testament..
I don't know either how R' Riskin would rule on the means of destroying just the Christian additions ("new testament"). It seems clear that any uses of the divine name don't call for burial; according to him it's ok to burn them. I don't know if it is obligatory to burn them or if any means of disposal is fine for those books.