Your AHC--at any time prior to the present date, create a world in which dispensational Christian political activism in the Western world (albeit it could be elsewhere too, I suppose) has adopted animal advocacy as one of its central, core causes that everyone associates with it. It can either be added onto the causes that evangelicalism is associated with today (i.e. abortion, sexual morality, human trafficking, etc.) or it can replace one or more of them.
You can bring this about however you want--a pro-"creation stewardship" school of Biblical exegesis becomes more popular than in OTL, there is some specific event that occurs that links animal welfare or animal abuse with a known evangelical cause--any divergences or butterflies you want to use are fair game!
--Bonus points if at least one major party Western presidential or prime ministerial candidate runs as a pro-animal-rights evangelical in a competitive democratic election.
--Major bonus points if one or more other major branches of world Christianity (Orthodoxy, Catholicism, Lutheranism) are brought into the evangelical animal-advocacy fold.
--Ultra-uber bonus points if evangelical animal activists are able to successfully fuse with more traditional, i.e. more left-wing oriented animal-rights entities like PETA and various environmental activists and together form a massive bloc of influence in the Parliament or Congress of a major country.
Note:
I don't see this as being that far-fetched. In fact, I'm going to declare this, preemptively, one of my easier AHCs.

We see bits and pieces of this right now, in quite a few places--albeit, admittedly, informally and not in an organized fashion.
MalcontentRex