Do active duty service members have the right to political protest?

Service members have the right to attend political protests, however, in doing so they are restricted to attending as a person as opposed to a representative for the force under which they serve.

For example, it's fine for an Army service member to attend a political rally, so long as he/she is not dressed to represent the Army. If a service member dresses in a way that purposefully makes the person seem like a representative of their armed force, (IE; that the Army as a whole supports the political movement) then disciplinary action may be taken.

You can read more about service members' rights to political activities on the Department of Defense's page at the link below: Political Activities by Service Members of the Armed Forces, Feb. 19, 2008.