Rosenburgs were not convicted for treason, but espionage.
The judge convicting them worked along with the prosecutor on the bar to make sure that they got a clean cut, and more easily prosecutable charge of _espionage_ instead of original treason. But yes, his ultimate reason was his personal insecurity about seeing his fellow Jewish American giving the public even more reason to doubt the loyalty of Jewish Americans (given how all things were at the time...)
Excerpt from wiki.
> Kaufman is best remembered as the judge who presided over the espionage trial of Julius and Ethel Rosenberg and imposed their controversial death sentences. Roy Cohn, one of the prosecutors in the case, claimed in his autobiography that his influence led to Kaufman's being appointed to the case, and that Kaufman had imposed the death penalty on Cohn's personal advice. This claim has not been verified, although it has been shown that after Kaufman learned that the FBI and Justice Department opposed death penalties in the case, he asked the prosecution to withhold its recommendation before issuing his death sentence. In his summing up Judge Irving Kaufman was considered by many to have been highly subjective: "Judge Kaufman tied the crimes the Rosenbergs were being accused of to their ideas and the fact that they were sympathetic to the Soviet Union. He stated that they had given the atomic bomb to the Russians, which had triggered Communist aggression in Korea resulting in over 50,000 American casualties. He added that, because of their treason, the Soviet Union was threatening America with an atomic attack and this made it necessary for the United States to spend enormous amounts of money to build underground bomb shelters." [5] Kaufman said that he had gone to synagogue to pray before issuing his death sentence; this enraged Supreme Court justice Felix Frankfurter, who later wrote to judge Learned Hand, "I despise a judge who feels God told him to impose a death sentence," and also told Hand that he was "mean enough" to stay on the court long enough to prevent Kaufman from having a chance to take Frankfurter's place in the so-called "Jewish seat" on the Court.[4][6]