“Sinn Fein is a changed and changing party,” she says. “I understand it’s a gear shift for people to appreciate that the party is changing but that’s the truth, so the only thing I can say to people is bear with me.”

Image Referendum posters featuring Sinn Féin President Mary Lou McDonald are all over Dublin. Credit... Fran Veale for The New York Times

A relative of mine who lives in the North once had a gun put to his head by Sinn Fein. It rattled him enough that he said he would never become “a Shinner,” as Sinn Fein voters are called, sometimes pejoratively. I ask Ms. McDonald what she would say to a person — and there are many — who’d been caught in the crossfire of Belfast confetti before but who now, with the departure of Gerry Adams at the helm, may be up for grabs in elections.

“I’m not on a mission to convince anybody to forget,” she insists. “In Ireland, the whole issue of remembering, and memory, is associated for very obvious reasons with a negative impulse because people suffered across the board, including at the hands of the I.R.A. — I recognize and say that very clearly — and at the hands of the British state, and Loyalist death squads, and so on.

“But remembrance is also a positive thing,” she says, brightly.

Ms. McDonald grew up less than a hundred miles from the armed struggle, which saw more than 3,500 people killed between 1969 and 1998, in a middle class home in a tony section of south Dublin. Unlike many of her Sinn Fein colleagues, and to her political benefit, she lacks what the Irish call “the smell of cordite.” Still, she says the violence shaped her.

She hails from a staunchly Republican family and says her grandmother, Molly, whose brother was executed in an earlier struggle for independence, hugely influenced her. “She used to look up the road to the North and she had a real sense of connection with what was going on up there.

“I remember the morning the news came down that Bobby Sands died. I remember the hunger strikes,” but, she said, growing up in the South, “you didn’t have the British army on the streets.”

Among those who did, some view the lack of blood on Mary Lou’s hands as a lack of credentials.

“You see, you get it from both ends,” she says. “On the one hand, you’re criticized for being too Republican, and then you’re criticized for not being Republican enough.”