Former president Mary McAleese has said she is worried that if the Border between the North and the Republic hardens, hearts will harden too.
Dr McAleese expressed concern that Brexit may destroy the goodwill built up during the peace process.
Meanwhile Dr McAleese, who campaigned for a Yes vote in the same sex marriage referendum, says Pope Francis will have to be "very careful" when he visits Ireland next year about how he handles the issue.
"It was hugely endorsed by Catholics," she said.
"So there's a need for reconciliation there."
In an interview with the international Catholic weekly 'The Tablet', she added that Ireland has a "vested interest in ensuring that the relationship Britain maintains with the European Union is as strong as it can humanly be".
She stressed that membership of the EU played a huge part in improving relations between Ireland and Britain and that it was crucial at the time of the Good Friday Agreement in 1998. Without it, she said, there might have been a different outcome to the vote in support of the peace process.
Referring to that vote, Dr McAleese said: "I'm not sure if we had known at the time that Britain was going to pull out of the European Union and with it bring Northern Ireland out... that people south of the border would have been as quick to sign off on changing the Irish constitution, because it was easier to do that [as] we were all members of the European Union.
"It was an easier sell and nobody thought in terms of withdrawing from the EU, so now we are in a very, very different situation."