I am not sure how "effective" these groups are, since I haven't heard much about them litigating anything.
I could simply just be mis-informed.
People for the American Way
http://www.pfaw.orgThe Alliance for Democracy
http://www.thealliancefordemocracy.orgMAINstream Coalition
http://www.mainstreamcoalition.orgThe American Humanist Association
http://www.americanhumanist.orgThe Institute for Humanist Studies
http://www.humaniststudies.org/Fairness & Accuracy In Reporting
http://www.fair.org/United for Peace and Justice
http://www.unitedforpeace.org/The Council for Secular Humanism
http://www.secularhumanism.org---
Here are some more, but I don't know if they count as "liberal":
The National Association for the Advancement of Colored People
http://www.NAACP.orgThe Simon Wiesenthal Center
http://www.wiesenthal.com/2600 Magazine
http://www.2600.com