By the spring of 2017, the family had received more than 700 vulgar and hateful messages, including death threats, many referencing the Holocaust. Some phone messages consisted solely of the sound of gunshots.

The Southern Poverty Law Center filed the lawsuit on Ms. Gersh’s behalf in April 2017. Mr. Anglin sought to have it dismissed, and a magistrate judge, Jeremiah C. Lynch, ruled against him in May. Mr. Anglin filed objections to that ruling, which sent the case to Judge Christensen for additional review.

David Dinielli, a lawyer for the law center, said in a statement that Judge Christensen’s ruling on Wednesday “underscores what both we and our client have said from the beginning of this case — that online campaigns of hate, threats, and intimidation have no place in a civil society, and enjoy no protection under our Constitution.”

In a phone interview, Mr. Dinielli said that the Gersh family had notified law enforcement of the harassment, but there have been no criminal charges.

The organization now expects the civil case to go to trial. It has taken a long time because it proved impossible to serve Mr. Anglin with legal papers, Mr. Dinielli said. Mr. Anglin’s last known address was in Ohio, but his whereabouts have been unknown for nearly two years. He is still running the site, possibly from overseas.

His lawyer, Marc Randazza, said that Judge Christensen’s decision was dangerous for free speech.

“The rule we lay down for the Nazi applies equally to the civil rights activist,” Mr. Randazza said in a statement. “And that ruling, if it stands, is not going to be good for anyone who engages in common outrage culture. Maybe that’s a good thing, but I think not.”

The site has also faced two other lawsuits. Taylor Dumpson, the first black woman to serve as American University’s student government president, filed a suit in May. She became an online target after a real-life incident: nooses and hateful messages left on campus a day after her inauguration. The suit was filed by the Lawyers’ Committee for Civil Rights Under Law.