The religious aspect was an after-the-fact construct by church writers-total b.s.. The war was motivated based on the fact that the western magister militum Argobast allegedly murdered the western roman emperor, Valentinian II (related by marriage and patronage to Theodisius) and set up his own puppet emperor Eugenius.

On a practical level, the battle was very significant in that Theodisius stripped many of the limitanae troops from the frontiers, as well as the alps garrisons. The battle resulted in massive casualties on both sides and essentially neutered the western roman army. Some scholars estimate that between the Battle of the Frigidus and the previous civil war with the usurper Magnus Maximus, the western roman army lost 2/3 of its strength. This was a major factor in the need to enroll barbarian federate tribes and Stilicho's reluctance to engage in set-piece battles when he took over as magister militum of the west.

Theodisius was an incompetent commander (he was previously exiled for this reason). Between not being able to contain the goths after adrianople and his two civil wars, he nearly single-highhandedly destroyed the operational capabilities of the late roman army (at least in the west).

In short, the Battle of the Frigidus was a huge nail in the coffin for the western roman empire. it is unfortunate the history books do not discuss this battle or the tremendous negative impact the Theodisius had the roman empire. While he is lauded for "reuniting" the two halves following Frigidus; in fact, all he succeeded in doing was wasting away Rome's ever dwindling armies and setting up an inherent conflict between east and west by installing two rival regents that would eventually lead tot he dissolution of the west.