The IRA and Sinn Féin began to embrace a more Marxist interpretation of their struggle in the 1960s, particularly after Cathal Goulding became Chief of Staff in 1962. Orthodox Marxism is a bit of a weird fit ideologically for an ethnic nationalist organization, and a lot of the rank-and-file, particularly in Northern Ireland, were not happy with the idea of building working-class solidarity with Protestant communities. This was also an era of increasing sectarian tension in the North- "working-class solidarity" is an unappealing idea when mobs made up of largely working-class Loyalists are burning people out of their homes. This was one of the major factors that led a large portion of Sinn Féin activists and IRA volunteers to split off from the official organization to form the Provisional IRA and Provisional Sinn Féin in 1970. The new organizations embraced socialist politics and left-wing rhetoric, but their ideological self-image had a lot more in common with contemporary left-nationalist groups like the PLO or the Basque ETA. Despite technically being a "splinter group," the Provisionals quickly became bigger and more well-known than what came to be called Official Sinn Féin and the Official IRA (those who stuck by the old leadership and their orthodox Marxist interpretation of The Troubles). In time, Official Sinn Féin changed their name to Sinn Féin- The Workers' Party, then again to simply The Workers' Party (reflecting their non-sectarian ideology), but despite the name changes, they never attracted any significant support among Protestants, and were quickly eclipsed by Provisional Sinn Féin (without any major competitors for the name, now known simply as Sinn Féin). The Official IRA were players during the early years of The Troubles, but they were marginal compared to the Provisionals and declared a cease-fire in 1972. The 1972 cease-fire provoked ANOTHER split, this time the dissenters called their military wing the Irish National Liberation Army and their political arm the Irish Republican Socialist Movement. The INLA had some successes and some support during The Troubles, but they were never a serious rival to the Provisionals, particularly after they developed a nasty habit of killing each other off in internal feuds. Today, every group in Ireland that advocates for a united Ireland based on orthodox Marxist dialectic materialism is completely marginal. It's the same story as in many western European countries- hard-line communist politics enjoyed a brief moment in the sun in the turmoil of the 1960s, but have since faded into obscurity.

Source: 'A Secret History of the IRA' by Ed Moloney

As a Northern Irish citizen who has lost family to IRA atrocities, & having studied Irish History I know that the IRA of the 60's had a slight Marxist element due to the idea of the "grand gesture" of the failed easter rising. Many of those who fought in the E.R. were left wing. However the INLA was the more Marxist element if the republican terror network, Sein Fein is considered as close to a Marxist party in NI as possible as everyone in the party is apparently on the same wage & everyone is at the same 'rank' so to speak. As to Your question about the 1920's Irish Free State Govt. I believe your answer is best explained by reading into the Irish Civil War. This is when the IRA split over the terms of the peace treaty with the british govt following the bloody Anglo-Irish War. It is an interesting period of history but very little has been written on it due to the divide it has left in Ireland to this very day.