There is a petition going around demanding that, like the Republic of Ireland, Northern Ireland should have a referendum to bring about marriage equality.
I and the majority of LGBT+ groups in Northern Ireland are opposed to the idea, which was first muted by Sinn Féin in the run up the the referendum in the republic and here are the reasons why.
1. There is not need for a referendum to bring about marriage equality in any part of the UK. In the Republic of Ireland there had to be a constitution change to recognise marriage equality. The only way to do so, based on that constitution, was to hold a referendum. In Scotland a simply Bill was required in Holyrood and for England and Wales a Bill before Westminster was enough to bring about such change. Such a bill would still need to be brought before the Northern Ireland Assembly to bring about any change.
2. A referendum is not legally binding in the UK. A referendum does not necessarily have legal binding on UK legislators to bring about change. Admittedly often they do bring about the change or endorse the decision of the referendum but there actually is nothing to prevent the legislative body with responsibility. Indeed if such a referendum were to come about in Northern Ireland there is nothing to prevent a petition of concern being used, by let's say the DUP, the prevent subsequent legislation coming into effect.
3. Public debate is not as mature on this issue in NI as the RoI. Despite legalising homosexuality later than the North the Republic of Ireland is at a far more mature level of debate on this issue than the North. Yes there are some stupid and ridiculous comments made by some of those opposed in the Republic, but the level of the political debate between the politicians, even those who disagreed with their parties stance, was far more civil and factually based than the largest party in Northern Ireland has shown again the recent election and aftermath to be able to carry on over issues of LGBT equality.
4. Both the two biggest parties are viewing LGBT equality as a political football. I'm sorry to say this but since it was first mooted that NI should have equal marriage Sinn Féin's support has become as much of a political football as the DUP's opposition to it has. This is no more evident than the poor timing of the last debate in Stormont and the call for this referendum now. Most LGBT activists were certain that the time to strike next in Stormont to seek marriage equality should have been after the referendum result in the Republic was known. But Sinn Féin decided that the 28th April (ie during the short campaign for Westminster) was the time to put the motion before the Assembly for the fourth time. This timing was poor and could only have come from a party that did not consider Westminster elections to be important. Most LGBT activists with party affiliation outside Sinn Féin were too busy with the election to lobby MLAs and get into a big campaign on this occasion. While the DUP have in the past picked on Sinn Féin President Gerry Adams saying that equality is a Torjan Horse by which to beat the DUP I would say that recent actions overlooking the views of the LGBT community shows they do not really understand the nature of this equality.
The DUP meanwhile use their opposition to LGBT equality as a means to shore up their core vote, although having lost Antrim South to a pro-marriage equality Unionist and seen the Alliance vote pick up a great deal of the UUP vote in East Belfast it would appear it is a tactic that only has limited appeal.
5. Should a socially conservative majority have a say on minority rights? In the Northern Ireland Act we actually have a statutory requirement for the public bodies to allow equality of opportunity for various groups, this includes marital status and sexual orientation. Would such a referendum actually fit within the statutory obligations of our public bodies? I do not feel it does. Even though recent opinion polls are showing that there is now a majority in favour of supporting marriage equality here, there is a danger that the most socially conservative part of the UK could be ground down in a particularly heated campaign to vote no on the day. Also many LGBT people already know the sort of vitriol that some politicians or campaigners already direct towards us when our rights aren't the focus of a campaign, we can only envision it getting ugly if they were the sole focus. Also if the social conservatives were to squeak a narrow majority, it would set back any hope of reform for 10-20 years, when we are only trailing a couple of years behind the rest of the UK and Ireland at present. People's rights for equality should not be placed in the hands who have privilege to determine the extension of those rights.