Any relationship between Soldiers of different ranks, which is too personal in nature, will cause problems in a unit -- its simply a matter of time. The Army also prohibits relationships between certain categories of Soldiers, regardless of any command or unit affiliation.

Are people in the military allowed to date each other?

Military regulations chiefly regulate against dating between two soldiers of different ranks. Military policy in all branches prohibits all kinds of fraternization between soldiers of different grades; while the prohibited relationship is officer/enlisted solider, it also applies to any two different grades of soldier.