Federal Workers Told To Halt External Communication In First Week Under Trump Staff have been told

[Jacob Boehme]

4. Federal Employee Oath of Office

“I, [name], do solemnly swear (or affirm) that I will support and defend the Constitution of the United States against all enemies, foreign and domestic; that I will bear true faith and allegiance to the same; that I take this obligation freely, without any mental reservation or purpose of evasion; and that I will well and faithfully discharge the duties of the office on which I am about to enter. So help me God.”
(5 U.S.C. 3331)

Nothing here about giving up first amendment rights. Granted, Federal Employees cannot willfully break the law such as publishing classified information, etc. But they are not subject to an illegal gag order.