ACLU fear for their image and reputation  because they would lose credibility if their lovely Ambassador lose. 

They are rightly worried having protected and promoted an abuser for years. 

https://theblast.com/c/johnny-depp-amber-heard-ACLU-lawsuit-defamation-trial

The Johnny Depp and Amber Heard lawsuit has garnered the interest of the American Civil Liberties Union, and the organization has asked to file an amicus brief in the lawsuit to be an advisor on the case. But, Depp's team isn't having it.

the ACLU send a request last Friday to enter the case amici curiae.

Their involvement would be to assist the court by offering information, expertise, or insight that has a bearing on the issues in the case.

the crux of this case revolves around Amber's op-ed in the Washington Post where she seemingly calls Depp a wife-beater. The ACLU posted the article on it's website and worked, in some form, with Amber in making the public statement.

Depp's team is actually considering adding the ACLU as a defendant in the case for its connection to the publishing. The organization and anyone with knowledge may also be called as a witness.

Depp's lawyer Adam Waldman tells The Blast, "The ACLU, co-conspirators with Ms. Heard in her defamation against Mr. Depp, also today sought permission to file a "friends of the court” brief. Since the ACLU will be a fact witness, and possibly a defendant in their actual role as "friends of the hoax,” we have denied their request. Ms. Heard may have failed yet again in court, but she is succeeding at sucking a number of social movements that have hit rock bottom but are determined to keep digging into her scam."

It's unclear if the ACLU will go any further to be heard in the case.