The No campaign in Ireland got money from anti-gay campaigners in America. They also looked at anti-gay campaigns in some European countries like Slovakia and used those campaigns as inspiration really. The Prop 8 campaigners used children as a primary concern to repeal gay marriage and the Catholic church and associated No Campaigners used the same tactic.
The No campaigners were worried that once gay marriage went through, then there'd be a referendum on abortion-David Quinn, director of Iona Insitute actually stated this. So their aim was to campaign for no gay marriage and then the momentum for an abortion referendum would hopefully die down.
The Iona Institute is infamous in Ireland at this stage. There was a libel case involved a drag queen Panti/real name Rory O'Neill. He called some members of the Iona Institute homophobic on television and then the TV station was sued for libel-they paid out €85,000 in damages in total (!)
The No Campaign also argued about freedom of conscience-that someone shouldn't be made sell something to people if it went against their beliefs. There was a recent legal case in Northern Ireland whereby a cake shop refused to sell a cake with gay imagery to a gay man and then the gay man complained about them. The cake shop owners were known for being ultra- Christian and being against homosexuality so the gay man essentially set the owners up and deliberately targeted them but homophobia is widespread in Northern Ireland so I can't really blame him tbh.
But in Northern Ireland, it seems like the DUP (a political party which is Protestant) is more anti-gay than Catholics really. One of the DUP politicians Iris Robinson described homosexuality as "an abomination". Of course, this was before it was discovered that she was having an affair with a 19 year old boy (she was 61 at the time, I think) and there were rumours that she had dated his dad too at one point! The leader of the DUP, Ian Paisley was very militant in all his views and now his son Ian Paisley Jr is leader of the DUP party so it's unlikely that the LGBT community in Northern Ireland will get marriage equality any time soon.
The No campaign also cited a fear that Catholic teaching would be stripped away from schools as a concern in their literature. They're worried that the schools will be secularised and that the influence of the Catholic church is fading.
The Archbishop of Dublin, Diarmuid Martin said that the Catholic Church needs a reality check following the results of the gay referendum because so many young people voted "yes". He said that clearly, the message of the Catholic Church isn't getting through to young people. Again, this shows that the Catholic Church is worried about losing influence. Diarmuid Martin generally tries to be a "cool priest" by slightly softening his stanch, much in the same way that the current Pope tries to do but this approach is so equivocal and disingenuous. It's not fooling the LGBT community because the Catholic Church's teaching regarding homosexuality remain the same. Telling someone to be celibate their entire life is not the answer!