This past week, after attacks on two mosques in New Zealand that left 50 dead, the Islamic State appealed for retribution. Calling the shootings an extension of the U.S.-led military campaign against the group in Syria and Iraq, the group’s spokesman, Abu Hassan al-Muhajir, said they “should wake up those who were fooled and should incite the supporters of the caliphate to avenge their religion.” The faithful cannot stand by, he said, while “Muslims are burned to death and are bombed.”

His words were chillingly similar to those of Robert Bowers, the man accused of walking into Shabbat services at Tree of Life synagogue in Pittsburgh last fall and murdering 11 people. Bowers wrote beforehand that he believed the white race would be eradicated by Jews and Muslims. He obsessed over HIAS, a Jewish social services organization that helps resettle refugees, including Muslims, in the United States. “HIAS likes to bring in invaders that kill our people,” Bowers posted online before the rampage. “I can’t sit by and watch my people be slaughtered.”

Both alleged killers justified their violence as self-defense, needed because of the other side’s violence. That’s because white supremacists and violent Islamists are radicalizing in nearly identical ways — and they are feeding the fears and hatreds of one another. Following decades of U.S. military incursions in the Middle East, Islamist terrorists say white “invaders” imperil Muslims, and Bowers and Brenton Tarrant, the admitted New Zealand shooter, are convinced that they have to protect their people from “invading” terrorists. It’s a dynamic that has roots going back to Sept. 11, 2001, with Osama bin Laden calling the attack vengeance for U.S. military action in the Middle East: “We should punish the oppressor in kind, and we should destroy towers in America in order that they taste some of what we tasted and so that they be deterred from killing our women and children.”

This mutually reinforcing cycle suggests that more attacks from both sides will come, as each incident radicalizes a new cohort of believers. Political rhetoric around Islamist terrorism fuels the white-supremacist fixation on “white genocide.” Yet while law enforcement agencies and Internet companies are getting better at controlling the means of Islamist radicalization — the sites where beheading videos and propagandistic sermons proliferate — and jihadist terrorism in the United States is at an all-time low, white hate crimes have been steadily climbing for years: Every single extremist killing in 2018 had a link to right-wing or white-supremacist ideology, according to a recent study by the Anti-Defamation League. But unlike the threat from violent Muslims, many officials and political leaders seem completely uninterested in trying to stop white radicalization.

A police officer stands guard near Al Noor Mosque in Christchurch, New Zealand, on Monday. It was one of two mosques in the city attacked by a gunman who, before fatally shooting 50 people, posted an anti-Muslim manifesto online. (Carl Court/Getty Images) Police tape cordons off Tree of Life synagogue in Pittsburgh last October. The man accused of killing 11 people during services there had posted white-supremacist writings on the Internet. (Salwan Georges/The Washington Post)

LEFT: A police officer stands guard near Al Noor Mosque in Christchurch, New Zealand, on Monday. It was one of two mosques in the city attacked by a gunman who, before fatally shooting 50 people, posted an anti-Muslim manifesto online. (Carl Court/Getty Images) RIGHT: Police tape cordons off Tree of Life synagogue in Pittsburgh last October. The man accused of killing 11 people during services there had posted white-supremacist writings on the Internet. (Salwan Georges/The Washington Post)

When the Islamic State claimed responsibility for the 2015 attacks in Paris that killed 130 people, it described the French capital as a city of “prostitution and vice” and a “crusader” capital. Compare this denunciation with Tarrant’s manifesto, which contends that Muslims are bent on destroying his race, as evidenced by his own visit to the “cursed” Gallic nation. “In every French city, in every French town the invaders were there,” he wrote. “No matter where I travelled, no matter how small or rural the community I visited . . . for every French man or woman there was double the number of invaders.”

Siege narratives abound on both sides. “Very much like the Islamic State invoked crusader-era narratives throughout their propaganda war, the New Zealand shooter . . . left references to things like the 1683 siege of Vienna, the 1183 siege of Akko,” says Ben Decker, a research fellow at the Harvard Kennedy School of Government who tracks online radicalization. Those allusions mimic “years of Islamic State propaganda.”

That’s because it works, particularly among aggrieved people immersed in certain ideological climates. Lauren Manning, a former member of a violent neo-Nazi gang in Canada, says she was recruited on an Internet forum for death-metal music fans. Her recruiter began taking her for drives through areas of Toronto that were mostly populated by Muslims to demonstrate the “white genocide” notion. “I actually grew up in an all-white suburb, so I didn’t have a lot of experience with people who don’t look like me,” she says. “It was easy for him to say, ‘We’re being wiped out’ when we were walking through one of those places.”

On the other side, lone-wolf Islamist killers in the West say they are avenging invasions of their homelands and preventing the extermination of their fellow Muslims. After Omar Mateen, a 29-year-old security guard, walked into the Pulse nightclub in Orlando and killed 49 people in 2016, he told hostage negotiators over the phone that he needed America “to stop bombing Syria and Iraq . . . I feel the pain of the people getting killed,” he said. “Now you feel how it is.”

Jihadists and white supremacists alike absorb such beliefs online. Syed Rizwan Farook and his wife, Tashfeen Malik, who killed 14 people in San Bernardino, Calif., four years ago, pledged their allegiance to Abu Bakr al-Baghdadi, the leader of the Islamic State, who was happy to accept credit for the shootings. But the couple’s attack was not directed by officials in Raqqa, Syria, then the group’s capital. According to the FBI, Farook and Malik self-radicalized by consuming jihadist propaganda online. Bowers and Tarrant, too, connected with a worldwide network of white supremacists on sites like 4Chan, 8Chan and Gab, all social networks notorious for racist, violent material. Bowers’s favorite

YouTube videos glorify Hitler and obsess over the “extinction” of the white race; his posts there reek of paranoid bigotry.

Yet witness the different ways we treat the same problem. After San Bernardino, family members of the victims sued YouTube, Facebook and Twitter for inciting terrorism by allowing users to post Islamist propaganda. A judge threw out the suit, but the companies got much better at locating and removing such content. “These efforts have dramatically reduced the availability of ISIS propaganda and inhibited the ability of ISIS recruiters to work on social media,” says J.M. Berger, the author of “Extremism.” Meanwhile, after Pittsburgh — or Dylann Roof’s mass shooting in Charleston, S.C., or Elliot Rodger’s incel killings in Santa Barbara, Calif. — the same official actors seemed unsure of how to proceed. There was nothing like the organized effort to interfere with the process of Islamist radicalization online.

Security guards patrol outside the Inland Regional Center in San Bernardino, Calif., in December 2015. A Muslim couple, who had radicalized themselves by reading online material, fatally shot 14 people there. (Stuart Palley/For The Washington Post)

One problem is that violent Islamism and white supremacism receive different legal treatment in America. “It will never be a crime to be a white supremacist in the United States,” says Peter Bergen, the author of “United States of Jihad,” citing the First Amendment. But it is a crime to give material support to the Islamic State, “because ISIS is a designated foreign terrorist organization.” Which means that federal law enforcement agencies have much less freedom to monitor or prosecute white supremacists — even those belonging to groups like Atomwaffen, a relatively new, exceptionally violent neo-Nazi organization that has been connected to five murders and a bomb plot over the past two years. Many would-be mass murderers — such as Christopher Hasson, the Coast Guard lieutenant accused last month of plotting a terrorist attack against politicians and journalists — are charged with mere gun violations, which carry much shorter sentences than terrorism charges.

This disparity in legal designations also seems to affect de-platforming efforts by tech companies like Facebook and YouTube. Concerns about freedom of speech dominate the conversation around limiting white nationalism online, and the sites aren’t always sure what qualifies as white-supremacist propaganda. According to a Facebook policy leaked last year , “White nationalism and calling for an exclusively white state is not a violation of our policy unless it explicitly excludes other [protected characteristics],” which is of course what a white ethno-state does by its very nature.

Other difficulties include the sheer volume of hateful content and limitations of algorithms. After the New Zealand attacks, a debate inside Google about censoring Tarrant’s manifesto centered on the length of the quotations people were posting, since longer excerpts were harder for human moderators to spot, according to internal emails. And white supremacists are skilled at getting around various restrictions by employing codes and abbreviations others wouldn’t necessarily understand or flag, such as using “1488” as a veiled homage to Hitler. “It’s an evolutionary principle that’s adapted by all pathogens when they’re trying to infect a host,” says Joel Finkelstein, director of the Network Contagion Research Institute, which tracks hate speech online. “You create a chaotic, cryptic language that’s ambiguous that allows you to operate under the radar of the things that would detect you, like the immune system of a civil society.”

The result is that the white-supremacist presence online is fast outstripping that of the Islamic State and other jihadist groups, according to George Washington University’s Program on Extremism, permitting one form of radicalization to persist undisturbed.

Another problem is the lack of political consensus about the scope of the white-supremacist threat. President Trump, the leader of the executive branch and, ostensibly, all federal law enforcement, said after the New Zealand massacre that he doesn’t think white supremacy is rising globally. “I don’t, really,” he told a journalist. “I think it’s a small group of people that have very, very serious problems.” Compare that with the blame he placed immediately after the San Bernardino attack. “That looks like another Islamic disaster,” he told radio host Mike Slater. “ . . . No matter where you look, it’s the same thing. Then when I say we have to practice vigilance and we have to look at people — and whether you’re looking at mosques or not — we have to be smart.”

This double standard is understandably frustrating to Muslim advocates and community workers. “When a Muslim attacks somebody, you can paint our whole religion in a certain way, and there’s a lot of narrative that’s crafted around Islam in that sense,” says Arbazz Nizami, co-founder of the Sahaba Initiative, a nonprofit group that provides social services to the San Bernardino area. “But with white supremacy, it’s not tied back to Christianity.” No wonder the Internet is full of Islamophobic musings of the sort that propel racists like Tarrant and Bowers.

All this means that white hatred is the harder bigotry to choke off. “The same insecurities and grandiose sense of self-importance drives extremists from all ideologies,” says John Horgan, a psychologist at Georgia State University. “But white supremacy is a far more dispersed and deeply ingrained ideology in Western society. It will be far harder to defeat than jihadism.” Yet because the two causes are beginning to feed off each other, having separate standards for each one — removing Muslim radicalization, leaving white radicalism alone — cannot help extinguish either one. You can’t end one without ending them both. And so far, we haven’t really tried.

[CORRECTION: A previous version of this story gave the wrong name for the university where John Horgan teaches.]