The Islamic Empires were majority Christian for around 400 years after the conquests, of course they had interest. Christianity wasn't a European religion.
Many Christian theologians such as Sebeos saw Islam in eschatological terms, for example in regard to the '4 beasts' of Daniel: “And behold, a fourth beast, terrible and dreadful and exceedingly strong; and it had great iron teeth; it devoured and broke in pieces, and stamped the residue with its feet... this fourth beast, which arises from the south, is the kingdom of the sons of Ishmael.”
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John of Damascus: "There is also the superstition of the Ishmaelites which to this day prevails and keeps people in error, being a forerunner of the Antichrist."
Muhammad also seems to have been anticipating the 'hour' in the imminent future as part of his prophetic message.
The conquests later drove the iconoclastic movement in the Byzantine Empire, as they sought to consider why God had 'punished' them by allowing infidels to defeat them.
Eschatological fervour also increased as they approached the millennium of Christ's life, which many saw as a harbinger of the apocalypse. This is arguably one of the cause of the 1st Crusade, and especially the Peasants Crusade that preceded it.
In the centuries before and after the rise of Islam, eschatology was a major aspect of Abrahamic religious thought. This may have led to the rise of Islam, and the rise of Islam certainly didn't make Christians less concerned with the apocalypse.