“The events of Charlottesville require any judge, any police chief and any legal group to look at the facts of any white-supremacy protests with a much finer comb,” said Mr. Romero.

The revised policy marries the 97-year-old civil-rights group’s First Amendment work with the organization’s stance on firearms, which aligns with many municipalities and states that bar protesters from carrying weapons.

“If a protest group insists, ‘No, we want to be able to carry loaded firearms,’ well, we don’t have to represent them. They can find someone else,” Mr. Romero said, adding that the decision was in keeping with a 2015 policy adopted by the ACLU’s national board in support of “reasonable” firearm regulation.