What the EU is doing makes perfect sense.
They have a long list of species that are causing issues in certain areas within the EU but not others. The Irish are getting hung up about the rules concerning sika, but really this legislation isn't being introduced to sort an Irish problem, it is to prevent those small populations of wild sika deer elsewhere in Europe from developing into the same intractable issue that is seen in Ireland and Scotland. The regulations impose restrictions on keeping, importing, selling, breeding and releasing these species.
The EU declared muntjac and grey squirrel invasive in 2016 while UK was still signed up to Europe, it made little difference in the UK but it certainly has helped reduce the number of muntjac introductions that were occurring in Ireland, Belgium and France following the rule change, and made it much easier for the Irish to legislate an open deer season for the few muntjac that did appear.
Nobody expected the UK on foot of EU rules to attempt to eradicate it's muntjac, nor will the EU or Irish government be able to affect sika deer numbers other than making it easier for them to relax open seasons. This obviously wasn't an issue for the UK regarding muntjac, which had no closed season anyway. However the rapid expansion of sika on the island of Ireland (Tipperary, Clare, Galway, Mayo, Cavan and Antrim) wasn't by range expansion it was by the very means that will be banned if sika are added to this list. Putting sika on the invasive list should have happened years ago.
Other mammal species were being traded and released around Europe. Raccoons were sold as pets and are destructive when feral as they are in much of Northern Europe. The Irish should be grateful that they are listed as invasive within the EU.
Whitetailed deer were introduced into Finland in the 1930s and for years tipped along causing few problems. More recently numbers have exploded, whitetails are starting to show up in Czech Republic and a few other places. Expect them to appear on the EU invasive list soon, again Finnish hunters will get excited, locally nothing much will change, but it will be harder for some estate owner in France or somewhere to get hold of breeding stock and release them, as happened with muntjac.