The Yes Equality group has called the hacking of the Youth Defence website a 'despicable' and 'disrespectful' act.
The homepage of the Christian pro-life group was yesterday replaced by a photo of the pro-same-sex marriage mural on Dublin's George's Street.
The Dublin mural, called "Our Nation's Sons", shows two men hugging in a promotion of gay rights.
It came just a day after another pro-gay marriage mural - depicting two women - was defaced on Dublin's South Richmond Street.
Both sides of the debate are launching new public campaigns, with just five weeks to go until polling day.
Yes Equality spokesperson Grainne Healy is calling for a respectful debate.
She says hacking should have no place in the referendum campaign.