Mr. Bannon himself seems fine with that description, telling Mother Jones last summer that Breitbart was now “the platform for the alt-right,” a loosely organized group of mostly young men who believe in white supremacy; oppose immigration, feminism and multiculturalism; and delight in harassing Jews, Muslims and other vulnerable groups by spewing shocking insults on social media.

To scroll through Breitbart headlines is to come upon a parallel universe where black people do nothing but commit crimes, immigrants rape native-born daughters, and feminists want to castrate all men. Here’s a sample:

“Hoist It High and Proud: The Confederate Flag Proclaims a Glorious Heritage” (This headline ran two weeks after a white supremacist massacred nine black churchgoers in Charleston, S.C.)

“Birth Control Makes Women Unattractive and Crazy”

“Gabby Giffords: The Gun Control Movement’s Human Shield”

If you don’t find the headlines alarming, check the reader comments. Or take a look at who’s rejoicing over Mr. Bannon’s selection. The white nationalist Richard Spencer said on Twitter that Mr. Bannon was in “the best possible position” to influence policy, since he would “not get lost in the weeds” of establishment Washington. The chairman of the American Nazi Party said the pick showed that Mr. Trump might be “for ‘real.’” David Duke, former imperial wizard of the Ku Klux Klan, called the choice “excellent” and said Mr. Bannon was “basically creating the ideological aspects of where we’re going.”

Mr. Bannon is in some ways a perplexing figure: a far-right ideologue who made his millions investing in “Seinfeld”; a former Goldman Sachs banker who has reportedly called himself a “Leninist” with a goal “to destroy the state” and “bring everything crashing down.” He has also called progressive women “a bunch of dykes” and, in a 2014 email to one of his editors, wrote of the Republican leadership, “Let the grassroots turn on the hate because that’s the ONLY thing that will make them do their duty.”