The 7th to 10th century Arab/Muslim conquests swept through large parts of the World. Levant, Persia, North Africa, North India, Iberia, and more.
My question is, why are they all major Muslim populations except Iberia?
Reconqustita and Spanish Inquisition are an easy answers. What I mean is how did they last 800 years under Islamic influence, without overwhelmingly becoming Muslim like everyone else.
Well, first we have to consider that Muslim rule did not last 800 years in all the Iberian Peninsula. The beginning of the Reconquista is traditionally put in the 8th century, when the northern kingdom of Asturias was estabilshed after the battle of Covadonga, just a few years after the Muslim conquest! By the 1200 AD more than half of the Peninsula was under Christian rule. So, it's 800 years of Islamic influence just for Andalusia.
Then, we have to consider the different policies of the Christian and Muslim states in Iberia about "infidels" and conversion.
Conversion to Islam was encouraged but not compulsory: Christians and Jews, and "people of the Book", could live in Iberia but had to pay a tax. The converts of "Christian" descent were the Muladi, and gradually merged with the Muslim of Arabic-Berber descent. Alongside the converts, many communities of Christians, the Mozarabs (=arabized), thrived.
Also the Iberian Christian kingdoms acted a certain degree of tolerance; the Mudéjares, Muslim subjects, were allowed to stay in Iberia.
So, between the VIII and the XV centuries we have on both sides subjects of both religions (or rather all three, considering the thriving Jewish communities), though encouraged conversions and emigration contributed to a growing homogeneity. By 1249, the only Muslim state is the Emirate of Granada: only there the majority of the population in Muslim and Arab-speaking.
In 1492 we have the end of the Reconquista: the whole of the Iberian Peninsula is under Christian rule. The Treaty of Grenada accorded certain rights to the Moors and a kind of tolerance, but the pressure to conversion was growing; in 1499 a rebellion led the Spanish rulers to revoke the Treaty and force the Muslims into either exile or conversion, (just like the Jews were forced some time before, in 1492). The converts, or Moriscos, suffered in the course of the 16th century mistrust, marginalization, deportation and eventually expulsion.
The great expulsion occurred under Philip III, between 1609-1614, after which apparently a few thousand Moriscos remained in southern Spain, almost completely blended with Christianity and Spanish culture.
Here you can read an outline of the Reconquista (including the Repoblaciòn, the resettlement of Christians in the conquered lands).
Briefly, the main reason of the failed islamization of Iberia is that Islamic rule there was neither complete nor stable, especially in the North. In the south the active anti-islamic policy of the Kingdom of Spain assured, conversely, the de-islamization of Andalusia.