Employees of the federal government by law are guaranteed the right to refrain from assisting a union. See 5 U.S.C. § 7102 (federal employees generally); 39 U.S.C. § 1209(c) (postal employees). (U.S.C. stands for "United States Code." To access the United States Code, click here.)
This means that you cannot be required to pay any dues or fees to the union in violation of your religious beliefs.