. . . The Catholic Church, for example, makes moral statements on the treatment of animals under the idea that animals belong to God and humans are commanded to be shepherds of creation. It does not place animals at the same level as humans, . . .
And there might be a way to square this circle!
Okay, so Catholics in particular have talked about being good shepherds for generations, and probably with some positive effect, as well as other Christians of all stripes although perhaps to a lesser extent. And there were earlier animal rights / animal welfare movements, such as establishing the Society for the Prevention of Cruelty to Animals around ? 1900.
But Peter Singer's essay "Animal Liberation" in the April 5, 1973, issue of
The New York Review of Books did jump-start the modern animal rights movement.
http://www.nybooks.com/articles/1973/04/05/animal-liberation/
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Two other ways utilitarianism might contribute to public movements:
1) From the perspective of the 1960s, people do feel for soldiers both sides, but mainly just for wars from way back when like the First World War. And it might really help to have a here-and-now theory saying it's good and proper to sympathize for soldiers from both sides. And if that's too much a challenge, at least try to sympathize for the families. It's a little bit like the Bruce Lee idea, my enemy, myself.
2) A number of '60s radicals played the macho card and basically claimed they were more macho than the police and the entire system. For example, at the 1968 Democratic Convention in Chicago, although the police may have been 70% responsible, some of the activists certainly did their 30%. Some guy gave a speech and said, if there's going to be blood, let it not just be from our side. And the members in the violent groups certainly liked to posture that they were more macho than the police.
Now, the ideas of civil disobedience and nonviolent resistance redefined courage in some ways. If there was a second theory also redefining courage, perhaps playing off the first redefine and also the conventional views, that could have been a very big deal.