As the week began, I planned to write this column about some implications of Barack Obama’s Sunday night Oval Office address. I noted that he devoted about one-fifth of this 13-minute speech to pleas that Americans not discriminate against Muslims.

“It is the responsibility of all Americans — of every faith — to reject discrimination,” he said. “It’s our responsibility to reject proposals that Muslim Americans should somehow be treated differently.”

At one level, this is an anodyne statement. As a general proposition, discrimination by religion is against the best in American tradition and the letter of American law. George W. Bush, you might recall, made similar statements in the days after Sept. 11, 2001.

But as events have shown then and since, both presidents “misunderestimated” — to use a verb apparently coined by Bush — the American people.

Yes, there have been incidents here and there when Americans have acted violently or rudely to people they have perceived to be Muslim. But they are exceedingly rare in a nation of 322 million people. Government statistics show that “hate crimes” are directed much more frequently against Jews, the target of prejudice throughout the ages, than against Muslims.

Both presidents showed a lack of confidence in the ability of ordinary Americans to carry in their heads two ideas seemingly in tension. One is that most violent terrorists these days are Muslims (our leaders may claim that they aren’t true believers in Islam, but the terrorists obviously don’t agree). The other is that most Muslims aren’t terrorists.

But it turns out that ordinary people are entirely capable of understanding that not everyone in a certain category behaves according to stereotypes, even those based on statistical facts. This is not actually a difficult concept. Fans know that most professional basketball players are black, but that nonetheless some whites are better players than some blacks.

There was another objectionable aspect to Obama’s Sunday night speech. “It is our responsibility to reject religious tests on who we admit into this country,” he said. That was a partisan slap at Republicans who suggested that priority in admitting Syrian refugees should be given to non-Muslims.

But no nation is under an obligation to admit foreigners to its territory, and the U.S. Constitution prohibits a “religious test” only for public officials.

American asylum law provides preferences for those persecuted for their religious beliefs, as Yazidis and Christians have been by Islamic State forces. For many years American law provided for special treatment for Soviet Jews. Religious tests, in appropriate circumstances, are entirely consistent with American tradition and humanitarian principles.

As noted, earlier this week I was prepared to write more along these lines. But then on Monday came the announcement that, in the words of a campaign press release, “Donald J. Trump is calling for a total and complete shutdown of Muslims entering the United States until our country’s representatives can figure out what is going on.”

A Trump spokesman initially said the ban would cover “everyone.” But it turned out later that the candidate would make some exceptions. Muslim U.S. military personnel stationed outside the country would be allowed to return. As would Muslims who are U.S. citizens.

Trump’s proposal was denounced by former Vice President Dick Cheney and by rival presidential candidates including (in alphabetical order) Jeb Bush, Chris Christie, Lindsey Graham, John Kasich and Marco Rubio. Ted Cruz said he disagreed with, but deftly declined to criticize, Trump.

I think Trump is “misunderestimating” the American people in much the same way as Obama. Where the president seems to fear the possibility of widespread violence against Muslims (or those perceived as such), the presidential candidate evidently sees a widespread consensus that Muslims are so likely to be dangerous that it is unduly risky to allow any to enter the country.

This seems to me to get recent history wrong. “If this guy doesn’t look like an Arab terrorist, then nothing does,” the ticket agent who let 9/11 hijacker Mohamed Atta pass through security recalled thinking, “but it’s not nice to say things like this.” Neighbors of the San Bernardino terrorists noticed peculiar goings-on but didn’t report them to authorities.

It seems that many Americans, out of a “misunderestimated” reluctance to discriminate by religion, have difficulty making the distinctions — or discriminations — needed to identify terrorists. That’s a problem not easily solved, and Obama’s and Trump’s “misunderestimates” aren’t helping.

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