Mrs. James almost sputters—“You can tell that I struggle even to find the words”—when I ask what she thinks of the New York Times’s “1619 Project,” which attempts “to reframe the country’s history, understanding 1619,” when the first slaves were brought to Jamestown, Va., “as our true founding.” That dubious history, Mrs. James says, hurts the cause of racial reconciliation. “It does harm because it creates a false narrative about what the real problem is, and if you don’t understand what the real problem is, you can’t come up with real solutions,” she says.

Chandler Junior High School in Richmond, Va., admitted its first two black students in 1960. A year later 30 entered the school, one of whom was seventh-grader Kay Coles. Now known as Kay Coles James, president of the conservative Heritage Foundation, she remembers students pricking her with pins and a teacher making a remark about “brownies.”

“This country has changed, and I have witnessed that change,” Mrs. James, 71, says in a phone interview nearly 60 years later. Mrs. James, who as a teenager participated in a march after Martin Luther King Jr.’s assassination, sympathizes with those Black Lives Matter protesters who are “genuinely grieving and heartbroken about how race is being handled in our country today.”

That view has drawn some fire from the right. In a May 30 FoxNews.com op-ed she asked: “How many more black people must die, and how many more times will statements of sympathy have to be issued?” She argued that “racism is still a problem in this country” and exhorted readers to “speak up and reject the racism and division in their own communities. . . . Racial equality is something that every one of us, regardless of skin color, must work toward on a daily basis.”

Fox host Tucker Carlson accused her of writing a “long screed denouncing America.” She responds tactfully, noting that she respects Mr. Carlson’s journalism. “It was disappointing,” she says, “that he did not know me well enough to know that I would never call America a racist nation—that he read that somehow as a screed. I thought it was a very thoughtful thing that both acknowledged that there is a problem but acknowledged as well that America is the only nation on earth that I know of that in its exceptional way has been gifted with founding documents and founding values and principles that allow us to address the flaws as they arise in our country.”

In our interview Mrs. James reiterates the point that America still struggles with racism: “It is inconceivable to me that there are those who believe that race is no longer a problem in America.” A few years ago, she says, young men in a pickup truck at a Richmond intersection called her by a racial slur and demanded to know what she was doing there.

Yet she rejects the idea that “institutional” or “systemic” racism persists. Thanks to “great strides” in the law, she says, the system is “only as racist as the individuals who occupy it”—though she hastens to add that some of them could “use some heart surgery.”

She chides those conservatives who disdain racial concerns as part of a liberal agenda: “One of the things that I’ve heard is that if you acknowledge the problem then you are playing into the left’s narrative. And I want to say: But it’s not their narrative! We should take it back! It’s our narrative. There would be no civil-rights legislation were it not for the Republican Party. Who led the fight to abolish slavery in this country?”

Conservative values and principles “exclude racism,” she insists, citing her own position as an example: “If I were walking into a progressive think tank I would have to do the calculation and determine: Were they trying to check some boxes, am I a product of their identity politics, did they pick me because I’m black and because I’m a woman? Being a conservative I have the comfort of knowing that at best that was an afterthought.”

But Mrs. James wants conservatives to acknowledge that black Americans contend with both bigotry and disparities. “We can’t have a conversation if they”—protesters—“believe that you don’t even see, understand or acknowledge the problems that we face in this country,” she says. “The difficult part is acknowledging the realities of what’s going on and yet saying that we believe as conservatives that we have real answers to those problems.”

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