Nonprofit organizations must file a Form 990 with the IRS and make this document publicly available (past 3 years). You can learn a lot about an organization from information required on the 990.
Other ways to discover information on nonprofit organizations.
The activist's almanac : the concerned citizen's guide to the leading advocacy organizations in America, HN55 .W35 1993 (maybe there are some other good books near this one too)
Explore digital archives to locate background information and understand the history around your issue. Here are some examples. Discovering whether or not an archive exists on your topic is often a matter of discovering a reference to it in a book, catalog, guide, or from another expert.
Use directories and indexes to discover names of organizations by topic, their websites, and how to find out more about them.
NTEE Codes provide a way to search for organizations by broad topic according to how they are classified by the IRS as tax-exempt organizations. A good way to identify codes is to search the NTEE Definitions with the link below.
Some potentially useful codes for this class are
I05 Crime & Legal-Related; Research Institutes & Public Policy Analysis
R30 Intergroup/Race Relations
R22 Minority Rights
R60 Civil Liberties Advocacy
R Civil Rights, Social Action, and Advocacy
R05 Research Institutes and Public Policy Analysis
I50 Administration of Justice
I60 Law Enforcement
I99 Crime & Legal-Related N.E.C.