Yes. That said, there is a possibility you will get push-back from your agency. To be in the best legal position, you should be prepared to show that any protests or other free speech activities took place on your own time.
You may have heard that federal workers have fewer free speech rights than other people. It’s true that you do not have an unlimited right to discuss partisan or political topics while on the job. However, the U.S. Supreme Court has ruled repeatedly that Americans don’t give up their First Amendment rights simply by becoming public employees, as the ACLU notes in this fact sheet. You have the right to speak out on political issues on your own time.
Are furloughed employees’ rights limited?
Probably not. The law specifically states that furloughed employees are not allowed to work, even on a volunteer basis. Therefore, furloughed workers should not have to restrict themselves to protesting during non-work hours. Federal employees who are still working during the shutdown should treat their work time just as if they were being paid and, to be safest, refrain from protest activities during work hours.
Can I talk to the press?
As long as you are doing so as a private individual, yes. Keep in mind that you are probably not authorized to speak officially on behalf of your agency. If you are, you should be careful because your employer does have the right to limit your speech in connection with official business. However, you are free to speak about your own experience with the shutdown and how it has affected you.
Does the Hatch Act restrict my speech?
As you may know, the Trump administration issued somewhat controversial guidance earlier this year regarding the application of the Hatch Act to federal workers. The Hatch Act is intended to prevent partisan political activity by federal officials.
Since the Hatch Act only restricts your activities when you are at work, while on duty and when you are invoking official authority, you should be completely free to protest the shutdown or any government policy on your own time.
Be cautious about discussing internal issues
You should take care when discussing problems you are having with coworkers or with particular management decisions. These are considered internal issues and you could be taken to task for discussing them with outsiders or the press.
Ultimately, you should do your best to be aware of your agency or department’s policies about public protest, and you are safest if you restrict your activity to your own time. That said, you do have a First Amendment right to share your shutdown experience with the world.