(CNN) Its name paints an image of a group dedicated to protecting American ideals. But critics call it the opposite -- an intolerant hate group opposed to freedom of religion.

Now, with two gunmen killed outside one of its events, the American Freedom Defense Initiative is back in the spotlight -- once again, surrounded by debate.

Here's what to know about the controversial group:

It calls itself a human rights organization ...

The American Freedom Defense Initiative says it has several tenets, including:

• Freedom of speech, "as opposed to Islamic prohibitions of 'blasphemy' and 'slander,'" which quash open dialogue about jihad and Islamic supremacism, the group says.

• "The freedom of conscience -- as opposed to the Islamic death penalty for apostasy."

• Equal rights of all people, "as opposed to ... institutionalized discrimination against women and non-Muslims" in Sharia law, or strict Islamic law.

... but it's also listed as an extremist group

"All anti-Muslim hate groups exhibit extreme hostility toward Muslims," said the SPLC, which tracks hate groups.

"Anti-Muslim hate groups also broadly defame Islam, which they tend to treat as a monolithic and evil religion. These groups generally hold that Islam has no values in common with other cultures, is inferior to the West and is a violent political ideology rather than a religion."

The SPLC also describes the president of the Defense Initiative, Pamela Geller, as "the anti-Muslim movement's most visible and flamboyant figurehead."

But Geller fought back.

"Who designated the SPLC as a legitimate authority? They are a radical leftist group who targets patriots, vets and even GOP presidential candidates," she told CNN. "They have never named a jihadi group as a hate group."

(The SPLC named almost 800 hate groups in its annual report, all of which are based in the United States, not abroad. Though it lists no "jihadi groups," it does include the Nation of Islam and All Eyes on Egypt Bookstore, both of which include tenets of Islam in their teachings, as "active black separatist groups." The SPLC also writes occasional blog posts on "Muslim extremism."

It has a program called Stop the Islamization of America

Geller is the president of both, and of another group called Stop Islamization of Nations. Her website touts awards from Republican clubs as well as a Creative Zionist Coalition award for Jewish Heroism.

Among the groups' principles: "SION calls for an immediate halt of immigration by Muslims into nations that do not currently have a Muslim majority population."

It also calls for "surveillance of mosques and regular inspections of mosques in the U.S. and other non-Muslim nations to look for pro-violence materials."

It fought against the 'Ground Zero mosque'

Protesters demonstrate against the "Ground Zero mosque."

In 2010, Stop the Islamization of America rallied against the building of an Islamic community center near Ground Zero, where the World Trade Center's Twin Towers once stood.

"Building the Ground Zero mosque is not an issue of religious freedom, but of resisting an effort to insult the victims of 9/11 and to establish a beachhead for political Islam and Islamic supremacism in New York," the group said

"Ground Zero is a war memorial, a burial ground. Respect it."

In its protest against the center, the group drafted an ad campaign showing a plane about to hit the World Trade Center with smoke in the background. The ad then features what Geller called the World Trade Center "mega-mosque," questioning why it would be built there.

Daisy Khan of the American Society for Muslim Advancement said the facility would actually be a "community center with a prayer space inside."

"There is a lot of ignorance about who Muslims are," Khan said at the time. "A center like this will be dedicated to removing that ignorance, and it will also counter the extremists because moderate Muslims need a voice."

It's launched controversial ad campaigns on subways

A "Defeat Jihad" ad in a New York subway, placed by the American Freedom Defense Initiative.

In 2012, the Freedom Defense Initiative launched an ad campaign in the Washington subway system , which read: "In any war between the civilized man and the savage, support the civilized man. Support Israel. Defeat Jihad."

Jihad -- which means "struggle" in Arabic -- is considered a religious duty for Muslims, though there are both benign and militant interpretations of what it means.

Geller defended the message.

"We don't think it's controversial," she said at the time. "It's truth. Telling the truth now is equated with 'hate' and 'bigotry' in an attempt to silence and demonize the truth-tellers. That makes my ads all the more important."

It wasn't the group's first venture into public transit systems. The Defense Initiative has also drafted contentious ads for the New York and San Francisco public transit systems, though the ads in New York have been under litigation with the Metropolitan Transit Authority.

One ad depicted slain American journalist James Foley moments before he was beheaded by ISIS.

The ad read, in part: "IT'S NOT ISLAMOPHOBIA ... IT'S ISLAMOREALISM."

Foley's family asked Geller's group to pull the ads, which it did.

But Ibrahim Hooper of the Council on American-Islamic Relations said such ads are dangerous.

"These ads are targeted mainly at people who are not Muslims trying to get them to hate Islam and be hostile to Americans Muslims," he said.

It refuses to back down

A Garland police officer keeps members of the audience inside the Curtis Culwell Center in Garland.

On Sunday, the Defense Initiative was hosting a "Muhammad Art Exhibit and Cartoon Contest" in Garland, Texas, when gunfire erupted outside.

The group said it specifically picked Garland's Curtis Culwell Center, a school district-owned facility, because it hosted an event denouncing Islamophobia in January.

"The grand prize was $10,000," she said. "Then there was a people's choice award where people could vote online" for a $2,500 prize.

As the event was winding down, two men drove by the building, got out of their car and started shooting, Garland police said.

A security guard was shot in the ankle, and police returned fire on the gunmen, authorities said. Both gunmen died near the car. It's not clear what their motive may have been.

Geller said the shooting won't deter her group from hosting similar events in the future.

"I will not abridge my freedoms so as not to offend savages," she said. "Freedom of speech is under violent assault here."