Fiona Ryan, 33, and her fiancé Jonathan Mathis, 32, started receiving abuse online when the TV campaign was criticised by an anti-immigration activist on Twitter for showing a "multicultural version" of an Irish family.
While some social media users defended the family and reported the tweet by conspiracy theorist Gemma O’Doherty, others added their own racist and offensive comments.
The couple responded last week by calling for tougher hate crime laws and more regulation of social media in Ireland.
But on Friday Ms Ryan told public broadcaster RTE that a death threat had been made against her, her partner and their 22-month-old son Jonah.
“They are talking about harming and death to my partner and my child so I am not going to stay in a country [where] this is allowed,” she said. “I felt like we needed to leave.”
The couple, who met in London seven years ago, said they had decided to move out of the Ryan family home in County Meath and return to England.
Ms Ryan said she was shocked by the abusive comments sparked by the initial tweet from Ms O’Doherty, which referred to a far-right conspiracy theory about the “replacement” of white people and called for a boycott of Lidl.
“When I read through them all I kind of feared for my safety, for my son’s safety straightaway,” she told RTE.
“It was pretty harrowing to have to read through all that and I don’t think anybody should be subjected to that kind of online abuse.”
Mr Mathis, who grew up in Liverpool and the Cotswolds, said the abuse had been “a theme throughout my life”. He added: “These people don’t care, they are filled with hate and ignorance.”
Ms Doherty, who was banned from Youtube in July for promoting hate speech, has previously claimed the Christchurch mosque shootings were a “false flag” operation and retweeted the disgraced former newspaper columnist Katie Hopkins.