Am I protected if I want to place a political candidate's bumper sticker in my cubicle at a nonprofit?
Where the general, constitutional rules of free speech fall can depend on whether your employer is considered a government agency. In addition, you want to look carefully at any employment manual that may have been provided to you. Such manuals tend to set the parameters on what is considered "political activity."
In addition, you'll want to give some thought to whether it really is prudent to disclose your political preferences. If you work for the Brady Center on handgun control issues and are supporting a candidate who's endorsed by the NRA, that might not sit comfortably with your co-workers (free speech issues aside).
Speak to your HR director to get more guidance on permissible cubicle decoration.