There are many factors to consider. For a start the 1916 rising was a militarily failure, a disaster. It did however start to swing public favour for the IRA and against the crown.

Another main point would be the civil war in the 20s which split the country down the middle. On one side you had pro treaty forces fighting for the republic we have today and on the other anti treaty who believes that nothing but a full united Ireland including the six northern counties would do.

Its hard to say Ireland won as clearly as that when although we managed to get our republic, it came at the cost of six northern counties and a brutal civil war!

I believe the resulting political fracturing which ensued from the civil war led to political parties which were a lot less militarised and socialist.

Its also important to remember that general Michael Collins, which was the main leader of the IRA against the British and the pro treaty forces later on was actually belonged to fine Gael, and not sinn fein which is ( / was) he political wing of the real IRA during the "troubles" up north in the 70s onwards.

That's just my take on things, I'm open to correction which I'm sure many will oblige :)

The goal of the republican movement was to found a republic, they were a broad church who had members of all political and social backgrounds. For example the 1916 signatories contained Joseph Plunkett who was from a very affluent background and James Connolly who was a socialist.

After the 1916 rising the leaders were shot and the majority of the other participants were sent to prison. It was while they were in prison that two things happened.

1. Sinn Fein who the British had blamed for the rising became a political force as republicans flocked to join, Eamon De Valera the most senior survivor of the rising was elected leader while still in prison.
2. the Irish Republican Brotherhood a secret organisation that had been behind the rising began organising the prisoners into a new organisation called the IRA. Michael Collins who had been an officer in the rising was made head of the IRB.

When the prisoners were released the newly organised IRB/IRA leaders were sent throughout the country to organise the IRA and get ready for a new fight. Meanwhile Sinn Fein fought the 1918 general election and won a landslide. The Irish Labour Party decided not to stand against Sinn Fein to unite the republican vote.

Sinn Fein refused to take their seats in the UK parliament and in January 1919 they formed their own parliament, Dail Eireann and again declared independence. Later that day the IRA shot two policemen and the war of independence began. That lasted 2 1/2 years.

During all of this time, people had put aside political differences in their aim to form a republic, so socialists, communists, fascists, working class, middle class, upper class people all fought together. That is why Labour stood aside in the 1918 election.

After the war of independence the IRA and Sinn Fein split into pro and anti treaty sides, they fought a civil war which the pro treaty side won. The pro treaty Sinn Fein eventually became Fine Gael a centre right political party. The pro treaty IRA essentially became the Irish army. The anti treaty Sinn Fein refused to sit in Dail Eireann for a number of years, they then split into Fianna Fail which is now a centre right party. The remainder party kept the name Sinn Fein and retained their links to the IRA. Throughout the 1930s they became a socialist movement.

So the IRA contained socialists, but it was not a socialist movement until it became so small as to be completely insignificant.

In the 1960s the IRA and Sinn Fein split into provisional Sinn Fein and IRA and Official Sinn Fein and IRA. The Provisional wing are what people think of now when you talk of Sinn Fein and the IRA.

Official Sinn Fein became the Workers Party then Democratic Left and then merged into the Labour Party, they're left of centre but are not socialists.

Sinn Fein are a populist party with many left wing policies, but have no intention of making Ireland a socialist republic.

According to the internet, they are a constitutional republic with a parlimentary system.

Even if they were socialists why would that mean Ireland wouldn't be a constitutional republic with a parliamentary system?