For most of the century -and really right up to the conquest in AD 711/712- the armies of the Caliphate were still busy conquering and consolidating territory in North Africa. Tangiers and Ceuta, both of which would provide crucial launching points for the invasion of the peninsula, were not conquered until sometime between AD 705-710-- though raids on the Balearic Islands did begin following the Byzantine's final expulsion from Carthage in 698. The territorial acquisition of North Africa took up much of the second half of the seventh century and was concentrated on the consolidation of urbanized pockets and the establishment of communication networks across the mountainous terrain and marginal land between them. This took the form of military garrisons; for most of the century, the Arab Muslims would remain a minority in control of these urban pockets; the maps depicting vast swathes of territory under Muslim control are a bit deceptive in that regard.

Of course, that doesn't mean North Africa wasn't experiencing important social and religious change. The subjugation of Berber tribes and their subsequent conversion to Islam would prove crucial to the supply of manpower in the Caliph's armies in the western Mediterranean, and Berber forces would certainly have a role in the conquest of the Iberian peninsula. But this was an ongoing process, and the speed with which the conquests of the southern coasts of the Western Mediterranean took place meant that the regions from which the Arab-Berber armies launched their invasions were only themselves just beginning to undergo the cultural, social, and political changes that would see the Islamification of the region. There simply was never a prolonged standoff between Islamic North Africa and Visigothic Spain that would require a protracted resistance. Once Tariq ibn Ziyad turned his eyes on the Visigoths, the kingdom fell quickly (and perhaps unexpectedly, the Visigoths appear to have been divided and woefully unprepared for what they might have thought to be run of the mill raiding parties).

EDIT: If you are interested in reading more about early medieval Visigothic Spain and the Conquest, Roger Collins' two books on the subject, Visigothic Spain: 409-711 and The Arab Conquest of Spain: 709-797, are great introductions to the period

The given answers have misinterpreted the OP's question. OP is not asking about how the 8th century conquest was resisted, but why there wasn't an (apparent) islamization of the Iberian population post-conquest. One that would have ensured Iberia remained as Muslim to this day as Morocco or Iran. Why did the Reconquista happen, and why Iberia is the only one of the Ummayad conquests that is not still Muslim today.