Several other recent studies, including one by the authors of American Grace: How Religion Divides and Unites Us, rank Mormons and Muslims among the least liked U.S. faiths.
The "What It Means to Be American" poll found that a small majority (53 percent) say the country is safer now than before the 9/11 attacks. But attitudes toward Muslims are far less straightforward.
More than eight in 10 Americans say that self-proclaimed Christians who commit violence in the name of Christianity are not really Christians. By contrast, less than half (48 percent) say that self-proclaimed Muslims who commit acts of violence in the name of Islam are not really Muslims.
"Interestingly, we find that Americans basically have a double standard when it comes to evaluating religious violence," said Robert P. Jones, of the Public Religion Research Institute, which produced the survey with the Brookings Institution.
On the same question, disparities arose among political and religious groups.
Republicans (55 percent) were more likely to call the perpetrator of a violent crime in the name of Islam a Muslim than were Democrats (40 percent). At 57 percent, white evangelicals were far more likely to consider the perpetrator a Muslim than were Catholics (39 percent) or black Protestants (36 percent).
In general, the survey of 2,450 adults with a margin of error of plus or minus 2 percentage points paints Americans' attitudes toward Muslims as a complex picture of acceptance and wariness.
Nearly nine in 10 Americans agree that "America was founded on the idea of religious freedom for everyone, including religious groups that are unpopular." And by a 2-to-1 margin, Americans reject the idea that Muslims want to establish Islamic law in the United States.
But they are divided as to whether Islam is at odds with American values, with 47 percent agreeing and 48 percent disagreeing.
The poll's authors likened this ambivalence about American Muslims to the evolution of attitudes toward Catholics, who were once widely suspected for their loyalty to the pope, and Mormons, once widely reviled for their religious practices.
Brookings scholar William A. Galston said Muslims are now testing the nation's tolerance, particularly as they try to build mosques.
"The siting of Muslim houses of worship," he said, "has become the object of great controversy, which really goes right at the heart of religious free exercise."
The survey also notes differing attitudes toward Muslims between generations, with more than six in 10 young Americans (ages 18 to 29) reporting comfort with several expressions of Muslim religious practice, compared with fewer than four in 10 senior citizens.
The report uncovered more ambivalence on immigration and concluded that prospects for immigration reform face steep obstacles.
A slim majority (53 percent) takes a positive view of the influence of immigrants on American society; 42 percent said the growing number of newcomers threatens American values.
And while 51 percent of Americans said the nation should make a serious effort to deport all illegal immigrants, when asked a more nuanced question, a majority seemed to oppose such a policy.
Asked whether they favor an immigration plan that combines enforcement with deportation, or a plan that combines enforcement with a path to citizenship, 62 percent preferred to combine enforcement with a path to citizenship.
• Ninety-five percent of Americans believe all religious books should be treated with respect, no matter the religion.
• 16 percent of Americans believe that people in Muslim countries have a favorable view of the United States.
• Nearly half of Americans (including 51 percent of whites) believe discrimination against whites is as big a problem as bias against minority groups. About three in 10 blacks and Latinos agree.
• The biggest differences in perceptions about discrimination emerged between those who most trust Fox News and those who most trust public television, with nearly seven in 10 Fox News fans saying that so-called reverse discrimination is as big a problem as traditional discrimination, compared with less than one in four public-television viewers.