This appears to be a major search - probably through books on social movements, and also through very many databases such as Proquest Dissertations, Sociological Abstracts, Social Sciences Citation Index, JSTOR (full text journals many years back, but a fairly clunky search engine), America History and Life, and no doubt others.
I spent a couple of hours looking in some full text databases and on the web itself, hoping for a nice chart or graph to show up. The closest I got was in Academic Search Premier where the search: "social activism" and trends gets 8 hits; social and activism and trends gets 38 hits, including: Title:From Science to Multiculturalism: Postmodern Trends in Environmental Organizations. Authors: Ignatow, Gabriel(Department of Sociology and Anthropology at Bar-Ilan University in Israel, and Assistant professor, Department of Sociology at Koc University in Istanbul, Turkey). Source: Global Environmental Politics; May 2005, Vol. 5 Issue 2, p88-113, 26p, 9 charts, 2 graphs. This one has a chart "numbers of environmental organizations established worldwide, 1969-1995" and "Multicultural organizations established worldwide, 1945-1995. Other tables give names of these organizations, and dates founded. This is a very technical article, with 66 references, and much discussion of statistical methods used.
The Social Bases of Environmental Concern: Have They Changed Over Time? Subject(s): CORRELATION (Statistics); ENVIRONMENTAL protection; HYPOTHESIS; SOCIAL change; SOCIAL sciences -- Research; ACTIVISM Author(s):Jones, Robert Emmet; Dunlap, Riley E.Source:Rural Sociology, Spring92, Vol. 57 Issue 1, p28, 20p, 2 charts. This article has a chart "Trends in public support for spending on the environment 1973—1990" that was based on surveys of nationwide probability samples of @1400 people.
Other possible searches are: "social movements" and trends (106 hits), social and movements and trends (187 hits), "social movements" and statistic* (50 hits). All of these searches were from Academic Search Premier (Ebsco). If you are not near an academic library, most public libraries have Ebsco's Masterfile Premier database, which by way of comparison gets 60 hits for the search: social and movements and trends. Articles in Masterfile would tend to be less technical/scholarly, but like Academic Search, many of the hits link to full text online.
Google.com searches seem to get somewhat close, but nothing like a convenient timeline or chart. The search "social movements" "animal rights movements" trends gets 49 hits, including some 80 and 100+ page documents that talk about the history of social movements. Possibly there is a chart or timeline well buried in these. "social movements" "animal rights" trends timeline gets 119 hits, and looks like a very mixed bag. For a more technical approach, scholar.google.com gets 149 hits for: "social justice" "animal rights" history trends. But many Google Scholar hits will be links to articles ONLY available onsite at universities, etc., so you would not be able to browse through those unless you happened to be at a big academic library that subscribes to them.
The search: social movements and trends, in the database "America, History and Life" gets 38 hits, but once again, none that really jump out as potential sources of a handy timeline or chart. It looks like potentially a VERY long search to find such a chart or graph, unless you get very lucky on more web searches; or looking in books on social activism in such call numbers as JK1764..., HV4708..., or other subject areas that might show up from "words anywhere in the catalog record" or even "title words" searches like: animal human rights, animal civil rights, social animal rights, etc. Public libraries would very likely have many of these books, usually in Dewey call numbers like 179.3 (animal rights) or 322... and 323... (social activism, civil rights movements, etc).
Thanks,
Jim