The recognition of foreign divorces is a complex area of law. Because Ireland did not have divorce until 1996 we also had and still have a very conservative approach to the recognition of foreign divorces and the law has not been updated even since the 2019 referendum.
The primary rule from 1986 is that Ireland will only recognise a foreign divorce if one of the spouses is domiciled in the country which grants the divorce. This is easy enough to determine if two French people divorce in France. It is not so clear if an Irish person goes to live in the UK or USA for a short period and gets a divorce while there.
Domicile means residence in a country with the intention of making that place your permanent home. Prior to 1996 many couples availed of foreign divorces some of which may not be entitled to recognition because neither spouse was genuinely domiciled in the country which granted the divorce (as an accommodation address was used) or in some cases never even went to the country which granted the divorce. The Dominican Republic offered such a service.
Since 2003 there has been an EU regulation ( EC 2201/2003) on the recognition of divorce, separation and annulment orders within the EU (save Denmark). This regulation provides that each participating country of the EU should automatically recognise divorces, separations and annulments of other EU member States. Since Brexit there are new rules for the recognition of divorces granted in the UK and Gibraltar as set in the Family Law Act 2019.