The presidential race’s “Muslim moment” has arrived, and it is graphically laying bare, once again, the Republican dysfunction that is convulsing American government.

On the face of it, Mr. Trump’s refusal last week to silence a supporter who called Muslims a “problem” – and added that President Obama is a Muslim – would seem to have little to do with the potential gridlock in Congress this week. Nor would presidential candidate Ben Carson’s comment to NBC’s “Meet the Press” Sunday that “I would not advocate that we put a Muslim in charge of this nation.”

And yet these snapshots of Trump and Mr. Carson both have at least one thing in common with House Republicans’ threats to shut down the government – this time over federal funding to Planned Parenthood, an abortion provider.

They drive establishment Republicans fruitcake.

Fundamentally at issue in both the new shutdown talk and in the insurgent candidacies of Trump and Carson is a tension that has driven Republican politics since the tea party revolution of 2010.

Establishment Republicans want to win elections, Republican voters want to feel they are being heard.

Recent evidence suggests that, at crucial times and in important ways, the two goals have been mutually exclusive. But they are clashing dramatically on the presidential campaign trail and in Congress this week.

Recent polls have found that 43 to 54 percent of Republicans think Mr. Obama is a Muslim, and only 45 percent say they would vote for a Muslim. Some 63 percent of Republicans want the main focus of United States immigration policy to be stopping the flow of immigrants and deporting those already here. And 53 percent support defunding Planned Parenthood.

All are in contrast with the broader American population, and by wide margins.

In other words, to give many Republican voters what they want on several key issues is a recipe to win House races in safe, localized districts, but to risk losing broader races for the Senate and White House. Indeed, Republicans’ success in the 2014 Senate elections began with rigorously weeding out antiestablishment tea party candidates.

Now, Trump and Carson are giving frustrated rank-and-file Republicans their voice again. And in doing so, they are forcing the Republican Party to come to terms with its own contradictions – an uncomfortable discussion the party has hoped to avoid for years.

Trump’s “willingness to say what other Republicans won’t has forced out into the open genuine policy debates among Republicans that had previously been shrouded in vagueness or imprisoned within party orthodoxy,” writes Greg Sargent of The Washington Post’s “Plum Line” blog.

Recently, the Republican establishment had also sought to tamp down potentially inflammatory talk on abortion. Comments about abortion likely lost Republicans Senate seats in Missouri and Indiana in 2012 and fed Democratic claims of a Republican “war on women.”

But a video from an antiabortion group has stirred the issue again, leading to calls for shutting down the government if Planned Parenthood is not defunded. The video shows a Planned Parenthood official talking about selling tissue from an aborted fetus. The process is legal as a part of scientific research, but the video – and the revelation of the practice – shocked many viewers, particularly for the casual tone of the conversation.

House Speaker John Boehner (R) of Ohio is strongly against abortion. But he sees more political damage than gain in shutting down the government over the issue.

So as he tries to head off a shutdown that he believes could damage the Republican brand more broadly, Republican leaders and strategists stand appalled by a Trump campaign they believe could damage the Republican brand more broadly.

The deeper concern is that there is no obvious “solution” to the disconnect between the Republican Party and many of its voters. The party cannot abandon its most passionate, partisan supporters, who can be reliably counted on to go to the polls, even in low-turnout midterm elections. But the direction of the country appears to be moving inexorably away from the worldview of these voters.

Latino voters were not a decisive voting bloc in the 2012 presidential election, an analysis by The New York Times found, but they tipped several key states into Obama’s column. And their influence is growing.

Meanwhile, Millennials, now the largest generation in the country, are significantly left of Republican orthodoxy on immigration, gay rights, business profits, and environmentalism, one Pew Research Center study finds. Another suggests that such differences might be culturally ingrained and persist even as Millennials age.

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In other words, there is evidence that what many Republicans of today want on a host of key issues runs counter to what the emerging America of tomorrow would appear to want. Establishment Republicans want to start pivoting to that potential future with candidates like Jeb Bush and Sen. Marco Rubio. Many Republican voters are having none of it.

Almost always, the establishment wins. But this year, the supporters of Trump and Carson – like the candidates themselves – are making a bold and unapologetic statement.