What is the etymology of "blameshift"?
Solution 1:
Probably "blameshift" is a back-formation from "blameshifting," which does have an entry at Dictionary.com. In general, compounds of an object and a gerund are more productive in English than compounds of an object and a finite verb form. Object-gerund compounds aren't always written closed; they can be open or hyphenated instead (see the examples like "mountain climbing" and "name-dropping" on the following page: hyphen in noun-gerund compounds).
The Google Ngram Viewer shows evidence for some use of "blameshifting" since around 1950, while not showing any evidence of use of "blameshift," "blameshifts" or "blameshifted."
As noted in Xanne's comment, the Google Ngram Viewer does indicate some use of "blame shift" and "blame shifts," but its a bit hard to tell whether "shift" is a noun or a verb in these cases. The Ngram Viewer itself actually seems to think that "shift(s)" is a noun in all of the examples of "blame shift" that it indexes, although it could be wrong. Looking though Google Books, I did find there is at least one example of a hyphenated infinitive "to blame-shift."
I don't know why some Wiktionary contributor thinks it is biblical. Without corroboration of this from some other source, I would just ignore it.