There are two main organizations which were involved in pushing back against some of the governmental abuses that arose in the 1920s.
The first of these was the American Bar Association (ABA). This organization was dedicated mainly to trying to ensure justice in the American legal system. The ABA felt that the Palmer had abused his power as Attorney General in ordering these raids. It also felt his actions were unconstitutional.
The second organization was the American Civil Liberties Union (ACLU). This organization was founded in 1920. It was dedicated to protecting what it saw as the civil liberties of all Americans. For this reason, it opposed the Palmer Raids strongly. The ACLU also pushed back against what it saw as unconstitutional assaults on the freedom of speech. It won a major victory in the case of Gitlow v. New York, in which it got the Supreme Court to rule that states had to abide by the First Amendment’s protection of free speech. It also pushed for the separation of church and state in the “Scopes Monkey Trial.” This group has continued to be important in civil liberties issues ever since.