The following list is not comprehensive, but includes some organizations dedicated to issues of social justice. For a longer list, check out the website for START (Study, Think, Act, Respond Together) - they have put together a list of social justice organizations separated by type, as well as links to organizations dealing with issues of economic, environmental, and health impact.
This TedTalk by Kimberle Crenshaw, who coined the term "intersectionality," gives context to that term and sheds light on how social justice problems are often multi layered and more complicated than a single source of injustice.
Content Warning: Videos (16:16 mark) at the end of the talk may be triggering to some.
The links above are a few arts organizations dedicate to social justice. If you would like to see more, please click on this link to read Social Justice and the Arts: Arts Organizations Partnering With Their Communities to Advance Social Justice, published by Open Buffalo and the Partnership for Public Good.