The Irish police will say "why are you bothering us? Ask an (Irish) judge like you usually do (via MLAT)". It is the judiciary that need to be involved first. Funnily enough that is also what former Irish attorney general and various senior EU officials have said - the correct approach is to use the MLAT, which is there for exactly this purpose. With a warrant from an Irish court the Irish police will be happy to help, should the Irish operators of the Irish data centre need a hand pushing the button in Ireland.
But the US doesn't want to use MLAT, it wants to end-run around it because they run into annoying problems like having to justify their request properly and whether or not their search is a search or a fishing expedition and stuff like whether the Irish user, in Ireland, has actually done anything illegal in Ireland.
Coincidentally,the UK police don't like MLAT process either and have said so in submissions regarding judicial limits of UK RIPA act. They run into annoying things like the US first amendment stopping them getting details of US users posting stuff on US servers that can be read in the UK and is not legal in the UK. If the DOJ succeeds in bypassing the MLAT process with this trick then some UK police forces will be right behind them ( and probably others elsewhere too). At least one of the amicus briefs points that out.
This will open up a big can of worms if it stands, extradition and MLAT treaties are a necessary process to protect both corporations and individuals from conflicting legal jurisdictions. Microsoft is not (just) saying "we can't, it's in Ireland", they are saying "we are not allowed to under the law of the country where the evidence is". Enabling the international rendition of data at the whim of any country's law enforcement doesn't physically extradite anyone, but it could easily end up making international travel a whole lot more interesting and risky. Be careful about exercising your first amendment rights to hate speech if you ever want a European vacation or business trip. Be aware that some EU jurisdictions are actively trying to outlaw anonymity and pseudonymity online...