NEW YORK — Faced with an angry backlash for defending white supremacists’ right to march in Charlottesville, the American Civil Liberties Union is confronting a feeling among some of its members that was once considered heresy: Maybe some speech isn’t worth defending.

Cracks in the ACLU’s strict defense of the First Amendment no matter how offensive the speech opened from the moment a counter-protester was killed during the rally in Virginia. Some critics said the ACLU has blood on its hands for persuading a judge to let the Aug. 12 march go forward. An ACLU leader in Virginia resigned, tweeting, “What’s legal and what’s right are sometimes different.”

“This was a real tragedy and we’re all reeling,” said Lee Rowland, a senior staff attorney at the ACLU’s headquarters in New York City. “Charlottesville should be a wake-up call to all of us.”

The backlash, reminiscent of one that followed the ACLU’s 1978 defense of a neo-Nazi group that wanted to march through Skokie, Illinois, a Chicago suburb with a large number of Holocaust survivors, set off a tumultuous week of soul-searching and led to a three-hour national staff meeting in which the conflict within the group was aired.

What resulted was an announcement that the ACLU will no longer stand with hate groups seeking to march with weapons, as some of those in Charlottesville did.