Final answer:
Federal civil service employees are prohibited from actively engaging in political campaigns by the Hatch Act of 1939, but they can join unions, contribute to campaigns, and participate in other election activities within set regulations.
Step-by-step explanation:
The question posed - regarding what federal civil service employees cannot legally do - is best answered by the Hatch Act of 1939. Under this act, federal civil service employees are prohibited from engaging actively in political campaigns and from using their authority to influence elections. However, they are not prohibited from being fired, belonging to a union, contributing to political campaigns, or being completely restricted in their election activities as long as they abide by certain regulations. It's important to note that the Hatch Act has gone through revisions to balance the rights of employees with concerns about political influences in the federal workforce.