Anti-Muslim sentiments dominated this past weekend’s news cycle. The coverage, of course, was sparked by Donald Trump’s refusal to correct a supporter who described President Obama as a Muslim and then said: “We have a problem in this country. It’s called Muslims.” Ben Carson then fueled the media’s focus on Islamophobia by suggesting that a Muslim should not be president because their faith is inconsistent with American values.

Many commentators have since argued that the American public should not have been surprised to hear either a Republican presidential candidate or one of his supporters express such beliefs (e.g., 1, 2, 3). The survey data, in turns out, would certainly support this suggestion.

After all, a previous Monkey Cage post showed that 54 percent of Republicans think that “deep down,” Obama believes in Islam. Likewise, a PPP poll from late August found that 54 percent of likely Republican primary voters thought Obama is a Muslim. A majority of the GOP also evaluates Muslims unfavorably, with Republicans and Republican-leaning independents rating Muslims substantially lower than any other religion. And less than half of Republicans recently said they would be unwilling to vote for an otherwise qualified Muslim candidate for president.

Those anti-Muslim beliefs have become a more potent force in Americans’ political opinions since Barack Obama ran for president. A number of studies show that attitudes about Muslims were much stronger determinants of vote choice for president in both 2008 and 2012 than they were in previous elections or than they would have been had John McCain face Hillary Clinton instead of Obama in 2008 (see 1, 2, 3). Anti-Muslim attitudes have also increasingly shaped Americans’ opinions about health care and congressional candidates in the Obama era (see here and here).

Trump and Carson had both appealed to such sentiments prior to their recent controversies, too. Trump, as many will remember, led the “birther movement” back in 2010 and 2011 that claimed Obama was not born in the U.S.; and political science research shows that the intertwined beliefs that Obama is both foreign-born and Muslim are caused in large part by ethnocentric suspicions of minority groups in general, and anti-black and anti-Muslim attitudes in particular (see: 1, 2, 3). Ben Carson, meanwhile, had made statements hostile to Islam before Sunday.

We should not be particularly surprised, then, that both of these candidates’ strongest support in the polls has come from Americans who question Obama’s Christian faith. For Trump, at least, this has been the case since he strongly championed bitherism during Obama’s first presidential term.

At the height of Trump’s birther attacks on the president in April 2011, we asked a nationally representative sample of 3,000 registered voters, who had previously been surveyed for YouGov’s 2007-2008 Cooperative Campaign Analysis Project (CCAP), what they thought of Trump. These exact same individuals had also been asked about Obama’s religion back in October 2008. The graph below displays net favorability ratings (favorable minus unfavorable) of Trump in 2011 based on respondents’ beliefs about Obama’s religion as of 2008.

There is a strong relationship between thinking Obama was a Muslim and support for Trump in 2011. The first panel of the display shows that respondents who knew that Obama was a Christian had an overwhelmingly negative opinion of Trump (-65) in 2011, but those who said Obama was a Muslim had a favorable rating of Trump (+20). The second panel shows that this strong relationship persisted even after accounting for partisan, ideological, and demographic factors.

An Aug. 28-30, 2015, PPP Poll of 572 usual Republican primary voters found a similarly strong relationship between rating Trump favorably and thinking that Obama is a Muslim:

The first panel of the graph above shows that Trump’s net favorability changed from -28 among the small minority of likely Republican primary voters who said Obama is a Christian to +39 among the majority of the sample who thought the president is Muslim. The same pattern is true for feelings about Carson.  However, the opposite pattern is true for feelings about Bush: Republicans who believe Obama is Muslim rate him less favorably than Republicans who believe Obama is a Christian.

The second panel shows a less pronounced relationship between beliefs about Obama’s religion and support for Trump and Carson in the Republican primary. Yet a clear pattern still emerges: Skeptics of Obama’s Christian faith support Trump and Carson more, and at Jeb Bush’s expense. Taken together, Trump and Carson received 25 percent of the vote from those who thought Obama is Christian and 51 percent  from those who think the president is a Muslim

To be sure, these results come with caveats. In particular, a number of factors that might be correlated with beliefs about Obama’s religion (e.g., distrust of government) could be responsible for its significant relationship with support for outsider candidates, Carson and Trump, in the PPP poll. These results do, however, suggest that Trump and Carson’s recent Muslim-related controversies are unlikely to offend their strongest supporters.