For some reason I've always thought of animal sacrifice as a trait of pagan religions, but when I was flipping through the Bible recently looking for inspiration I was struck by how many animal sacrifice references I found. So roughly when did animal sacrifice fall out of favor in these religions and why? I've not read the Quran, but did early Islam also include animal sacrifice?
I can't speak to Islam, but in the case of the other two, the answer is relatively straightforward.
For Christianity, it ceases almost immediately. Theologically, the New Testament texts depict Jesus as the final sacrifice fulfilling the role of the temple sacrifices, and obviating any ongoing need for animal sacrifice. This is seen clearly in, for example, the book of Hebrews.
I say 'almost' immediately, because there's no evidence either way whether the earliest generation(s) of Jewish background Christians continued to observe animal sacrifice practices in the Jerusalem temple.
In the case of Judaism, sacrifices pretty much cease with the destruction of the Jerusalem temple by the Romans in 70AD. The Hebrew Scriptures tie animal sacrifices to that temple and proscribe animal sacrifice in other settings. No temple - no place and no means to offer acceptable sacrifices. Hence, no ongoing animal sacrifice in post-temple-destruction Judaism