It's possible to knock out cellular network in relatively wide area and RF for example certainly capable of this. Even if they not target specifically cell phones.Cellphone disruption ( and landline, media) won’t affect the military very much but will for the civilian population. Without a reliable means to communicate with the public, confused civilians could easily be a problem for military operations.
But isn't the answer to this is army, who has communication, to establishing contact with civilian population(you know leaflets, direct contact with civilian authorities in area etc.) and guide them to stay at home for example, while military provide relief when needed?
Military can't actually shrink responsibility in this case.
In Israel we have Home Front command, that do guide civilian population. During the operation in enemy territory, army do similar things to a lesser extent.