The introduction event should have explained this to you somewhat.
Also, check out some of the Eire threads, they have a lot of details.
The core issue is that Eire society and politics was radically different from any other in the world. The model of hierarchical authority that was largely constant across the rest of the world simply did not exist in Eire. To use some contemporary jargon, Eire was a kind of anarcho-socialist collective.
Consider the following:
1. As much as they had a king, he was elected, and could be thrown out as well.
2. The king's powers were quite limited. He could not even increase taxes in any way, for example, nor change ANY laws. He was effectively just the commander of the armies and the head of state, undertaking foreign policy. His other work was ceremonial and ensuring the maintenance of core public facilities, including roads and bridges and hospitals.
3. The same was true of regional and local authorities. There was NO hereditary nobility and the concept was entirely foreign in Eire society. Anyone who had authority in Eire (except the Church, naturally) was elected, and could be thrown out.
4. So, no feudalism, and everyone a freedman with an equal right to be elected to any office. Written down in law. Low aristocracy, low serfdom, low centralization and you with no legal authority to change any of that.
So, that means that if you want to play an Eire that works in a more
generic middle ages way, then you would have to suggest a storyline wherein someone of a Napoleonic stature emerged who would have the personal Charisma and military brilliance to foreever change Eire society. The culmination of that period would be the removal of the flag gaelic_law, meaning that different events would and would not trigger for Eire.
Such a storyline and event series would created a long, long period of civil unrest, and there would need to be quite a substantial 'payment' in game terms for undertaking that path.
There are two natural periods where it might occur. One is during the 'civil war' in the early 1500s, the other would be the Gilchrist O'Neil period. There could be an action_c in one of those where this aforementioned brilliant leader takes over Eire and leads it in a new direction.
Otherwise, you need to accept that we won't create events where you can chose to have the Caliphate turn Catholic, nor an
equally radical concept such as Eireann law changing at the whim of the player. And if Eire is therefore not to your taste, that's cool, play a different country.