Islam as a rising social force and political power in the first few centuries of its existence forced the Church to respond, and in ways that were not healthy for religious unity across Europe. The Schism between the East and West threw the Church on its heels, and forced it to turn increasingly to the western powers of the time for support, money and protection.
I think #2 does have a point about the way that Islam helped Christianity by giving it a common enemy that could it identify itself in opposition to. This throughout history has been a method of uniting and unifying forces. Having an enemy to go against is a very helpful product.
The rise of Islam was key in the fall of the Western church and rise of the Eastern Orthodox church. The Muslims were key in the fall of the Roman Empire and the diminishment of the power of the church in the west. This split led to the feudal system in the West and the Byzantine empire in the East. Eventually the empire in the East would also fall to the Muslims, leading to the Crusades, whose sole purpose was to regain the "Holy Land" for the church.
My problem with Post #2 here is that Islam started to rise in the 600s and the Crusades didn't for another 400 years or so. So I guess this depends some on how long you are saying the "rise" of Islam lasted.
I think a more immediate consequence was the entanglement of the Church with the Frankish kings -- what would lead to the Holy Roman Empire. When the rise of Islam cut off the Eastern Roman Empire from the West, the Church had to rely completely on the powers in the West for support and that meant the Franks. Once the popes turned to the Frankish kings for protection, it meant that the kings were going to try to use the Church to bolster their own power. This ended up leading to all sorts of problems between the Church and the kings as to who would have what sorts of power. I see this as the major impact of the rise of Islam.
Perhaps the greatest impact of Islam is that it became the identifiable enemy of the Church. It was directly responsible for the launching of the Crusades; which were to rid the Holy Land of the Muslims. Although Islam considers Christians and Jews "people of the book," who should be protected; Muslims were historically considered only Infidels by Christian Europe. It was only after Muslim armies captured Jerusalem and threatened Constantinople that Urban II preached the First Crusade.
Also, after the marriage of Ferdinand and Isabella, the Reconquista forced the remaining Muslims in Spain to either convert or leave the country. Interestingly, most chose to leave. Those who remained, the "Moriscoes," were treated widely with suspicion.
So, Islam was the personification of evil to the Church, and gave it a physical enemy to attack; even though both worship the same God.