The Department of the Army owns a federal registration for WEST POINT covering multiple goods and services. West Point Graduates Against The Waris an organization of West Point graduates against the war. The Army has sent them a demand letter.
Some cases involving trademark use by advocacy organizations include Brach van Houten Holding v. Save Brach’s Coalition, 856 F. Supp. 472, 31 USPQ2d 1786 (ND Ill 1994) (no online version available), where the trademark owner sued the union for using the BRACHS mark to name an ad hoc anti-management group. See also International Assn of Machinist and Aerospace Workers v. Winship Green Nursing Center, 96-1206 (1st Cir. Dec. 30, 1996), where the union sued the trademark owner for using the union’s trademark in informational material during the dispute.
However it seems that WPGAW’s focus is not really West Point and its policies. This case may fall more cleanly into fact patters such as Playboy Enterprises, Inc., v. Wells, 279 F.3d 796 (9th Cir. 2002), which hold that you may truthfully identify prior affiliation providing that such use is not confusing.
Practice pointer: It would appear that the NY Times reported on the existence of West Point Graduates Against The War because of the demand letter.

Duke Law & Technology Review iBrief: “Injunction Junction: Remembering The Proper Function and Form Of Equitable Relief In Trademark Law.”
Abstract: Injunctions are supposed to be among the most extraordinary remedies in the American judicial system, yet they have become anything but rare in trademark litigation. Although the unique nature of trademark protection may explain the frequency of injunctive relief, the process by which this relief is issued is rapidly devolving into rubber-stamping by the courts. This iBrief argues that courts should (1) recommit themselves to the principles of equity before granting injunctions and (2) seriously apply the specificity requirements of Rule 65(d) of the Federal Rules of Civil Procedure to avoid overly broad orders.