Some NATO contries have agreements with the US on how to handle service members, not sure if all of ICE/DHS falls under that, but it is there to keep US personel at military bases safe from their own actions and the target contries laws. The US pinky promises in the agreements to prosecute the persons under US law if the country just hands them over with no fuss. Under current conditions in the US, I take that to mean that US service members can commit any crime in any nation with such an agreement without any consquences.

On top of that there is the ‘invade the Hague act’, but that is just for war crimes.

And I don’t think any EU country have the death penalty (even “life” generally means like <20 years).

Does Italy have the same agreement with the US like Sweden does where, at least soldiers, are allowed to commit unlimited crimes in their country because the US “promise to totally” charge them back home? Then letting ICE in is asking for trouble.