But Republicans are not averse to exploiting the Democratic divisions. The Republican Jewish Coalition purchased a $530,000 ad campaign in June accusing Scott Wallace, a Democrat running in Pennsylvania’s First Congressional District, of anti-Semitism. Mr. Wallace ran an organization that dispensed more than $330,000 in grants to boycott, divestment and sanctions groups; Mr. Wallace has disavowed the movement and said he did not exercise authority over those funds.
The Republican Party of Virginia has laid into Ms. Cockburn, calling her a “virulent anti-Semite,” a charge she hotly contests.
In California, Representative Duncan Hunter, a Republican under indictment on charges of campaign finance violations, is trying to tar his Democratic opponent, Ammar Campa-Najjar, with a grandfather who masterminded the 1972 terrorist attack on Israeli Olympic athletes in Munich. Israeli commandos killed Mr. Campa-Najjar’s grandfather long before Mr. Campa-Najjar was born.
The liberal Jewish group J Street condemned that effort on Wednesday as “one of most ugly, racist campaign ads we’ve ever seen.”
Ron DeSantis, the Republican nominee for Florida governor, has accused his Democratic opponent, Andrew Gillum, of having ties to anti-Israel groups, citing financial support he received during his primary race from Dream Defenders, an organization that backs boycotts, divestment and sanctions, and a speech Mr. Gillum gave two years ago at a Muslim advocacy event welcoming the Council on American-Islamic Relations to Tallahassee. Mr. Gillum denies supporting the boycott and divest movement.
“Anyone trying to use Israel as a political wedge and football doesn’t have Israel’s best interest at heart and should be ashamed of themselves,” said Representative Debbie Wasserman Schultz, Democrat of Florida, calling the accusation “revolting.”
Republicans say they will continue to push the issue.
“The fact that this is allowed to metastasize in the Democratic Party without any real pushback,” Mr. Brooks said, his voice trailing off. “It used to be one of the third rails of politics, especially in the Democratic Party.”