I am a permanent U.S. resident (a E.U. citizen).
I was a high school senior in the U.S. before I had my permanent residence card (J-2 visa thanks to scientist dad), and for our Government class, I had to spend a certain number of hours working for a political campaign of our choice. My immigration status was not at all a problem when I inquired about it at the time.
As a permanent green card holder, you are allowed to donate not only your time, but money as well (I am not sure about temporary green cards when it comes to donating your money).
This also may be of interest to you: last month I was hired as a poll worker in Seattle, even though I am not permitted to vote. Requirements for volunteering at elections vary, however‒here in Houston, only U.S. citizens can be poll workers.
posted by halogen at 8:15 PM on September 13