If printed out, this newsletter is your personal property and cannot legally be confiscated from you. “Possession of unauthorized material may not be prohibited.” (DoD Directive 1325.6 Section 3.5.1.2) You have the right to posses one copy of any publication. You should be aware that if you distribute publications without the express permission of your commander you may be punished. Material can be impounded if a commander determines "that an attempt will be made to distribute". (DoD Directive 1325.6 Section 3.5.1.2) Having more than one copy of a publication is usually considered to be an attempt to distribute.
You have the legal right under the Uniform Code of Military Justice to attend protests and other political events provided that you are not in uniform.
You also have the right to publish your own publication as long as the work occurs off-base, on your own time, and with your own money and equipment. (DoD Directive 1325.6 Section 3.5.4)