What if Islamic empires had conquered Britain, Spain, France, Dutch, Germany?There was an Islamic empire in Spain (and Portugal, though for less time I believe). Actually though, it would probably be more accurate to say that an Islamic power began to colonize -- in about the 700's CE (or AD) in what would eventually become Spain as we know it today. To a certain extent it might not be entirely an overstatement to say in fact that the presence of (and the various ways of "dealing with"; from accommodation, to warfare against) an Islamic power, in its central and southern areas, was part of the proto-Spanish national formative experience in a sense.
What would happen if...? Well, it seems that the Islamic presence was struggled against by some of the Spanish (or the "proto-Spanish" if you will) from nearly the start. As the Catholic Christians from the more northerly Iberian regions fought the Muslims almost immediately upon arrival, and eventually retreated into separate kingdoms in the north. Christian realms, which were basically at a state of ongoing tension (if not to say ongoing warfare) for generations with the Muslim polities to their south.
Eventually, after hundreds of years and gradual but steady gains by the Roman Catholics, the newly united Crown(s) managed to fully conquer the remaining Muslim emirate in the south of the peninsula. This would have been right around 1492 in fact. Around the time that the Spanish monarchs sponsored a certain Genoese explorer who thought he would make it directly to the East by heading west, and instead ran into a whole other world.
In Spain over the next period of time then, under King Phillip II, an edict of repression of all perceptibly Middle Eastern or North African cultural items occurred. Such as banning Arabic use in general (most Hebrew speakers were already gone), banning Arabic names, banning "Moorish" (that is, Muslim) attire, banning and perhaps even burning books in Arabic, and forbidding the practice of Islam entirely.
This harsh edict caused a revolt by the Muslims and the (ostensibly) former Muslims who had converted to Catholicism. A revolt which the Crown eventually forcibly suppressed and which basically led to the mass expulsion of all Muslim and "former Muslim" elements from the peninsula.
Forced conversions and as mentioned mass expulsions, first of Jews then of Muslims, had taken place. Most, if not nearly all, Jews and Muslims (and the supposedly Catholic-converted Jews and Muslims) were expelled from the peninsula by about the 1620's or so. Some areas were heavily depopulated as a result. Spanish business and trade suffered, particularly in certain industries. However they did bring in "Old Christians" (that is, not recent converts' descendants) from the northerly regions, to repopulate these coastal or southern/southeastern areas.
Most of the "Moriscos" (i.e., "former Muslims" who had at least nominally converted to Christianity), or their descendants, wound up in North Africa. Which is, in a sense ironically, the region from which the first Muslims had entered Spain hundreds of years prior.
As for Spanish Jewry (or "crypto-Jews"), they may have wound up in places like southern Italy (which was under the Spanish Crown as well for hundreds of years but was less directly subject to Inquisitorial practices), or the Spanish parts of the Americas in particular. Or North Africa, or even as far abroad as Greece or Turkey. Both Greece and Turkey were under the Islamic Ottoman Empire at the time. Some of the expelled Iberian Jews actually sought out the dhimmi -- or, "protected minority" -- status in the Muslim Ottoman realms. Sensing that it was safer to be a tribute-paying minority there than it was trying to live under Catholic rule at the time.
It did conquer Spain actually! For 7 centuries, until Ferdinand and Isabella kicked them out. Andalusia, 'Al andalus' was prosperous with relatively much religious freedom and acceptances (although Jews and Christians were not allowed to display to much of their faith in the public domain; like church bells and stuff). But this tolerance created high levels in science, art and architecture (e.g. El Alhambra) that are still unique...
Btw. The Dutch live in the Netherlands, not in Dutch or dutchland or something like that