No, we entered a common trade market. We're not even part of Schengen. We're an odd fish in terms of EU membership overall given our geographical position, size, and CTA with the UK.
We are the only EU member state that are obliged to hold public referendums on Treaties. Ratification of the Treaty in all other member states is decided upon by the states' national parliaments.
Ireland, Netherlands, and Luxembourg also have veto powers when it comes to EU wide regulations.
In short, if we didn't have so many of our national parliament trying to appease the bureaucrats in the EU so they could land cushy numbers in the European Parliament for retirement, you'd see a lot more sabre rattling from Ireland regarding EU interference.
Well thats the rub, by being a part of the EU they are effectively semi-sovereign. Not to sound like a Brexiter