“My personal take is it’s a statement of where we are in this country,” said Michael Feinstein, the chief executive of the Bender Jewish Community Center of Greater Washington, in Rockville. “There’s some thought amongst some people that hate speech and hate crimes are O.K. and anti-Semitism is O.K., and I think that is reflective of sort of the political discourse that we’ve had in this country.”

Mr. Feinstein said about 300 people had been in the Rockville center when the threat was made, including about 200 preschoolers. After the threat in Delaware, parents were called to pick up preschool and day school students. In South Carolina, Mr. Abels said staff members and patrons attending exercise classes had to leave. About three hours later, he said, the authorities said it was safe to return, leaving many to wonder what had happened.

“It could be anything from hate groups to a terrorist situation,” Mr. Abels said. “I think it’s probably more on the hate group side, because it was just a scare.” He said he believed it was “designed to be psychologically disorienting and scary and just disruptive.”

Jerry Silverman, the president and chief executive of the Jewish Federations of North America, said the threats were part of a disturbing trend toward normalizing hate speech. It was less than three years ago that a former Ku Klux Klan leader killed three people outside Jewish facilities in Overland Park, Kan. And in November, after the presidential election, the Anti-Defamation League posted a warning about a reported uptick in hate speech and anti-Semitism.

Some members of the alt-right, a far-right fringe movement that embraces elements of anti-Semitic, racist and anti-immigrant positions, perceived the victory of President-elect Donald J. Trump as validation for their cause and have become increasingly visible in recent months. Mr. Trump, who has a Jewish daughter and son-in-law, has disavowed the alt-right.