Our trouble is that all contemporary narratives of the period are produced in a religious environment, and so intrinsically portray a religious and moral message no matter the events they portray. The Anglo-Saxon Chronicle, therefore, often refers to the Danes or Vikings as "Pagans", aping an earlier British/English literature trope seen in Gildas and Bede wherein the arrival of the then-Pagan Anglo-Saxons in Britain was a punishment from God for the sins of the British. It's no surprise therefore, that both the ASC and Asser's Vita Ælfredi both emphasise Alfred's piety and fierce Christianity as deciding factors in the victory of the English.

The situation, of course, is somewhat more nuanced, and largely secular. Alfred, naturally, had a personal stake in maintaining his rule and the territorial integrity of Wessex. He also had a personal stake in the fate of neighboring Mercia as well. His father had allied with the Mercians, his wife was Mercian and his daughter married the ealdorman of the Mercians in *c.*883. The Vikings, while a very real threat to the peace and prosperity of England, were also a very convenient catalyst for the political unification of England, and a prime opportunity to increase the power of the Cerdicing dynasty. A powerful external threat acted to drive Mercia and Wessex, who had been at war as recently as the 820s and only formed a fragile alliance in the 840s, firmly together to the extent that by 920, the two kingdoms merged entirely. The actions of the Vikings and the establishment of the Danelaw also effectively removed political obstacles to Wessex-led unification, replacing independent Anglo-Saxon kingdoms such as East Anglia and Northumbria with an amalgamated 'Danelaw' that must be liberated and restored to England.

Religion forms a very powerful motivator to your average ninth century man. No doubt that the English at the time did feel like their faith was under threat, as well as their lives and livelihoods, and the promise of divine assistance in a just war of defence against the 'Pagans' was both a staunch morale booster as well as a justification of conflict which could lionise Alfred as a defender of Christendom rather than as just a king fighting to hold his throne.

When Alfred defeats Guđrum c.878, he does force him to convert to Christianity, but this is as much because acting as his godfather puts Alfred in a very real and public position of personal and political superiority over Guđrum, as it stems from concerns for his immortal soul.

As an aside, in the tenth century, things become more clear. The unified - and Christian - English happily trade with the Hiberno-Norse, Danes and Hiberno-Norse through the ports of Chester and Bristol, while an early threat to Edward the Elder's reign comes from his own cousin, who leads a Viking army to Essex in an attempt to gain a throne he believes should have been his.

So, uh, basically mostly "3", but with a dash of both 2 and 4.

Some reading:

Stenton (1971), Anglo-Saxon England

Keynes and Lapidge (2004), Alfred the Great

Keynes and Blackburn (1991), Kings, Currency and Alliances

Molyneaux (2016), The Formation of the English Kingdom in the Tenth Century

Pratt (2007), Image result for the political thought of alfred the great The Political Thought of King Alfred the Great