On more than one occasion Mr. Peltz, who is Jewish, has encountered what he considered at least a whiff of antisemitism. He recalled that his arrival in London in the 1980s was greeted with a tabloid profile headlined “The Wild and Rocking World of Nelson Peltz.” The first sentence, he said, called him a “Jewish boy from Brooklyn,” and the British business establishment closed ranks against him.

Mr. Peltz, long a fierce critic of antisemitism, said he stepped down from his role as chairman of the Simon Wiesenthal Center in December because after 40 years in the position, it was time for a change. But The Wall Street Journal reported that he left after the center called for a boycott of Ben & Jerry’s. The center had deemed posts by the company’s chairman to be pro-Palestinian after the Hamas attack on Israel. Mr. Peltz is a board member of Unilever, the owner of Ben & Jerry’s.

His fellow billionaire Henry Kravis, the buyout pioneer, is one of the few Jewish members of Palm Beach’s old-money Everglades Club, but not Mr. Peltz. Mr. Peltz said he had “refused to set foot” in the club until it had a Jewish member and, now that it does, has had lunch there several times. (Mr. Peltz belongs to the Palm Beach Country Club, which has long accommodated members excluded from more restrictive Palm Beach clubs.)

Mr. Peltz’s reputation as a corporate troublemaker also cost him his longtime relationship with his Manhattan law firm, Paul, Weiss, Rifkind, Wharton & Garrison. In 2019, the firm cut ties with him even though he had been one of its biggest clients for decades. Paul Weiss handled his estate planning and other matters; a Paul Weiss partner left the firm to become his general counsel. But after Paul Weiss expanded its elite corporate practice in recent years, the firm told him that it could no longer represent activist investors, including him.

Mr. Peltz countered that he wasn’t an activist, he was a “constructivist” — someone who worked with management, not against it. He had never mounted a hostile takeover, he said, or even fired a chief executive. Paul Weiss was unpersuaded. “They dropped me like that,” Mr. Peltz said. “I was probably their oldest living client.”