No can of Coke for Muslim woman? American Islamic backlash simmers.

Since the aftermath of 9/11, American conservatives and liberals have diverged sharply in what they think about Islam. Two events this weekend, including a spat over an in-flight Coke, hint at how and why a backlash to Islam is evolving.

This weekend, a protest by anti-Muslim demonstrators with military-style weapons and an in-flight disagreement over a can of Diet Coke provided fresh evidence of a mounting Islamic backlash in America.

High-profile incidents have become familiar in recent months, with an outpouring of anti-Islamic sentiment on social media after the release of the surprise hit film "American Sniper," and a protest against an annual Muslim day of outreach at the Texas Legislature. A Mohammed cartoon drawing contest in Garland, Texas, last month, even provoked a failed terrorist attack.

Polls suggest that these flashpoints come from a decisive and growing split in how Americans see Islam. The current backlash is largely among conservatives, and it appears to reflect not just a fear of terrorist attack but also a deeper conviction that the tenets of Islam fundamentally prevent it from living peaceably with the modern world. The result has been a hardening of rhetoric.

Friday's protests were a response to last month's attack in Garland. About 250 demonstrators – many of them armed, some wearing T-shirts with profane anti-Muslim messages – gathered outside the Phoenix mosque where the shooters in the attack had worshipped. The organizer called himself a patriot standing up against the perceived tyranny of Islam.

Meanwhile on Sunday, social media was humming with the story of a Muslim scholar who had been denied a can of soda on a United Airlines flight because the attendant said it could be used as a weapon – though others on the flight had received cans, the scholar said. A fellow passenger also told the scholar: "yes you know you would use it as a WEAPON, so shut the **** up," she added on her Facebook page.

While the incidents point to activity on the anti-Muslim right in America, they also hint at its limits. Pro-Muslim counterprotests in Phoenix were reportedly just as large, and a Washington Post report spoke of anti-Muslim protesters whose minds were changed when they were welcomed into the mosque. Social media hashtags boycotting United Airlines and supporting the Islamic scholar have also sprung up.

In recent years, however, American opinions of whether Islam is more likely than other religions to promote violence have taken two very different tracks. From 2002 to 2003, the share of Democrats with that opinion spiked from 22 percent to 43 percent. But since then, the number has steadily declined to 29 percent in 2013, according to the Pew Research Center for US Politics & Policy. 

For Republicans, there was also a spike from 2002 to 2003. But since then, the numbers have continued to climb to 62 percent in 2013.

Earlier this year, Pew reported that conservatives – particularly evangelicals – viewed Muslims more unfavorably than every other religious group, including atheists. On a "thermometer" to measure warmth of feeling, Muslims got a chilly 33 degrees from conservatives; evangelicals a toasty 71 degrees. Liberals had Muslims closer to the middle at 47 degrees.

In this divergence, the rise of Islamic State appears to have acted as a stimulant. 

An NBC News poll taken shortly after the Islamic State's beheadings of two American captives last year found that 47 percent of respondents said that America was less safe now than before 9/11. The previous high – in 2013 – was 28 percent.

The spate of recent high profile anti-Muslim events has come since the rise of the Islamic State. But the Islamic State has no known operational capacity in the United States aside from attempts to inspire lone wolf terrorists from afar. And, by the best available data, right-wing extremists appear to have killed more people in America since 9/11 than have Islamist terrorists.

Instead, it is perhaps the Islamic State's apocalyptic brand of Islam – which embraces the notion that Islam cannot reconcile with the West as anything other than conquerors – that has most played into latent American fears.

The winner of the draw Mohammed contest, for example, told Jihad Watch that "any term other than Islam to refer to the enemy's ideology implies that Islam as such is not the problem, that only some deviant form of it is the problem. Every time we use a term other than Islam, we’re helping Islam."

Political activist Ayaan Hirsi Ali also became a frequent guest on conservative media after Brandeis University revoked its plan to give her an honorary degree. She has said "violence is inherent in Islam" and "Islam is the new fascism," according to The New York Times.

A groundbreaking piece on the Islamic State in The Atlantic took on the question of the group's "Islamic-ness" directly, suggesting that the rules of the caliphate in Iraq and Syria are drawn directly from and are consistent with the Quran. Other scholars have challenged that conclusion.

Contact with actual Muslims, however, has at times softened the cutting edges of the debate. In a Washington Post report on Friday's protests in Phoenix, Evan Wyloge writes:

Jason Leger, a Phoenix resident wearing one of the profanity-laced shirts, accepted an invitation to join the evening prayer inside the mosque, and said the experience changed him.

“It was something I’ve never seen before. I took my shoes off. I kneeled. I saw a bunch of peaceful people. We all got along,” Leger said. “They made me feel welcome, you know. I just think everybody’s points are getting misconstrued, saying things out of emotion, saying things they don’t believe.”

Paul Griffin, who had earlier said he didn’t care if his t-shirt was offensive, assured a small crowd of Muslims at the end of the rally that he wouldn’t wear it again.

“I promise, the next time you see me, I won’t be wearing this shirt,” he told one man while shaking his hand and smiling. “I won’t wear it again.”

To some, the backlash against Islam speaks primarily to the rise of Muslims as a visible – and visibly distinct – minority. By 2050, they will be the second-largest religious group in the United States (at 2 percent), outnumbering Jews, according to the Pew Research Center for Religion & Public Life.

"The good news is that everything that is said about Muslims today – that they are not American, that they are fearful, that they don't belong here – everything that was said about Muslims today were said about the Jews in the '40s and '50s, was said about Catholics at the end of the 19th century," Iranian-American author Reza Aslan told "The Daily Show." "And those two religions, through the passage of time, through the slow-building of relationships and the integration of story, became very much part of the religious fabric."