Striking is a self-destruct button for their careers.

Specifically, 5 U.S.C. §7311, specifies that federal employees may not participate in a strike, assert the right to strike, or even belong to a union that “asserts the right to strike against the government of the United States.” Driving the point home, 18 U.S.C. §1918 makes it a felony to strike against the United States or belong to a union that asserts the right to strike against the United States. What’s more, the Office of Personnel Management can declare an individual who participates in a strike unsuitable for federal employment. Forever. (Source)