WWE performers have long relied on patriotism and “us vs. them” narratives. In the 1980s, a tag team featuring the Iron Sheik and Nikolai Volkoff waved the flags of Iran and the U.S.S.R.; in the 1990s, Sgt. Slaughter, a onetime patriot, switched his sympathies to Iraq. Recently, Miroslav Barnyashev, a Bulgarian athlete who competes under the name Rusev, wrestled John Cena in a so-called “flag match”; the Stars and Stripes prevailed. But Mr. Dhesi has been elevated by the company at very specific moment. One of the pillars of President Trump’s campaign platform was to cut down on undocumented immigration, and his charged language often linked immigration with crime, spurring protests all over the country. This month, Mr. Trump unveiled a proposal to cut legal immigration in half.

Both Mr. Dhesi and WWE executives deny that his story line was politically motivated or designed to send subtle messages, even as the company has made a large investment in becoming a global product. The WWE is looking to expand into India, a country where sports entertainment is already popular, with a potential audience of 1.3 billion people. Its programming is available now in 180 countries and in 650 million homes, according to a spokesman. It is a publicly traded company and has attracted many big name sponsors, including Snickers and Mattel.

“We keep our finger on the pulse of pop culture,” said Paul Levesque, an executive vice president and a longtime performer, known as Triple H. “But we’re more worried about entertainment and pop culture than we are about politics and pop culture.”