To be fair, the organization still goes to bat for some causes that are associated with conservatives and free-speech absolutists, including the right to bear arms

Name one example (hint, you can't). From the ACLU's own website:

Given the reference to "a well regulated Militia" and "the security of a free State," the ACLU has long taken the position that the Second Amendment protects a collective right rather than an individual right. For seven decades, the Supreme Court's 1939 decision in United States v. Miller was widely understood to have endorsed that view. This position is currently under review and is being updated by the ACLU National Board in light of the U.S. Supreme Court decision in D.C. v. Heller in 2008.

Hey, it's only been 14 years; how's that review coming?