Donald Trump on Monday called for a “total and complete shutdown of Muslims entering the United States” in response to the recent attack in San Bernardino, California, which investigators believe was inspired by the terrorist group known as Islamic State. When Trump says “total and complete,” he means it: Trump’s campaign manager told the Associated Press that the ban would include Muslim tourists, and a spokesman told The Hill that it would even cover American citizens living abroad.

Some of Trump’s rivals for the Republican presidential nomination came out against his proposal (with varying degrees of intensity). Jeb Bush called Trump “unhinged” on Twitter, while Ted Cruz, campaigning in South Carolina, said he didn’t share Trump’s position but called for a three-year moratorium on accepting refugees from countries where Islamic State or Al Qaeda control territory.

It’s too soon to know how Trump’s proposal will affect the campaign; plenty of his past comments were ridiculed by pundits but failed to hurt his standing in the polls. But there are a few things that we do know about Americans’ views of Muslims, and Muslims’ view of their place in America.

Americans – especially Republicans – have negative opinions of Muslims: A 2014 Pew Research Center poll asked Americans to rate various religious groups on a 0 to 100 scale, with a higher score indicating more positive feelings. Republicans (including people who lean Republican) gave Muslims a rating of 33, on average — one point lower than atheists and far lower than any other religious group. Democrats had more positive feelings toward Muslims, but were still chilly; they gave Muslims an average rating of 47, slightly above atheists and Mormons and below other religious groups.

Republicans are also more worried than Democrats about Islamic extremism. A separate Pew survey last year found that 82 percent of Republicans were “very concerned” about the rise of Islamic extremism in the world, compared with 60 percent of political independents and 51 percent of Democrats. And Republicans were much more likely than Democrats to report believing that Islam is “more likely to encourage violence among its believers” than other religions.

Trump supporters may have even more negative views of Muslims. According to a Public Religion Research Institute poll conducted earlier this year, 77 percent of Trump supporters believe “the values of Islam are at odds with American values and way of life,” versus 72 percent of other Republicans (43 percent of Democrats said the same). Class and education make a big difference too: Two-thirds of white working-class Americans said Islam was incompatible with American values, compared to about half of white Americans with a college degree.

But Republicans may not support a religious test for immigration: The idea of basing immigration on religion is too new — at least in the modern mainstream political conversation — for much polling to have been conducted. But a Fox News poll last month did ask whether there should be a religious test for accepting Syrian refugees. Overall, Americans were strongly opposed: 64 percent of respondents said they believe a religion-based policy would be “shameful — There should not be a religious test for who is welcomed into the United States.” Among Republicans that percentage drops to 49 percent, while 37 percent said they thought “it makes sense — Christians in the Middle East have been targeted by Muslims and are not likely to be terrorists.”

The Fox poll didn’t break out results among very conservative Republicans, but among those who self-identify with the tea party, 38 percent said a religious test would be shameful, versus 47 percent who said it makes sense. Trump won the support of 29 percent of self-described tea party members in last week’s Quinnipiac poll, suggesting many of his core supporters might embrace his proposal.

American Muslims are concerned about anti-Muslim sentiments: Muslims are a tiny minority in the U.S. Less than 1 percent of Americans identified as Muslim in a 2014 Pew poll; most are either immigrants or the children of immigrants.

In a 2011 Pew poll, more than half of American Muslims said that being a Muslim in the U.S. had become more difficult since the Sept. 11, 2001, terrorist attacks. More than 1 in 5 reported having been called an offensive name or singled out by airport security, although more than a third said someone had expressed support for them. Some 6 percent reported having been threatened or attacked.

Only 15 percent of Muslim Americans in the Pew poll said that the Republican Party was friendly to Muslim Americans. That compares to 46 percent who said the same of the Democratic Party and 64 percent for President Obama. Moreover, 70 percent of Muslim Americans self-identified as Democrats or as leaning Democratic, versus only 11 percent who identified as Republicans or as leaning Republican.

The vast majority of American Muslims oppose violence: Trump’s press release cited a poll finding that many American Muslims support violence against Americans. But the poll was conducted by the Center for Security Policy, a group run by Frank Gaffney, whom the Southern Poverty Law Center describes as “one of America’s most notorious Islamophobes” and who once published a book titled “Shariah: The Threat to America.”

More credible organizations paint a very different picture. According to Pew’s 2011 poll, more than 80 percent of American Muslims said suicide bombings or other violence against civilians is “never justified.” (Just 1 percent said it is “often justified.”) Most American Muslims said there was little or no support for extremism among Muslim Americans.

But American Muslims are concerned that radicalism could become more common. Sixty percent said they were “very” or “somewhat” concerned about the possible rise of Islamic extremism in the U.S., and close to half said U.S. Muslim leaders had not done enough to speak out against extremists.

Leah Libresco contributed research.