The main action that Congress took against labor unions right after WWII was the Taft-Hartley Act.  The most important thing that this law did was to make it harder for unions to get members.  It did this by outlawing the "closed shop."  It made it illegal to make contracts that force a business to hire only members of a union.  (However, it was still legal to have a contract that said anyone could be hired but they would have to join the union after being hired.  This was called the "union shop" system.)   The act also made it possible for states to pass "right to work" laws that forbade the union shop system as well as the closed shop.