I would look at what Jack had to say, if you can obtain his work - not that I would necessarily put much if any stock in it.
The Church starting somewhere around 500 to 600 AD became involved in civil affairs as the Roman rule started to disintegrate, various tribes rose and fell in conquest, and the Church was the single surviving organization capable of providing a counter balance. By then significant parts of Europe had either been Christianized or were on their way to being so. Over time, the Church exercised more and more influence on rules, at times opposing those trying to ascend to the throne, and often being part of the entourage around a king and court, in part because they (particularly bishops) were the most educated - sometimes the only educated.
by the time we get to Luther, there are princes rebelling against papal and episcopal “interference” and seeking to reduce or ignore the power and influence of the churchmen. By the time we get to Vatican 1, the Church has largely been reduced to trying to rule the papal states and is under the protection of French troops. The troops leave for the Franco-Prussian war, the Papal States rebel, and try to take over Rome, leaving the Pope the “prisoner of the Vatican”
So we can see an arc of gaining influence, consolidation, and eventually a loss of influence.
Whatever the source was re: Islam by conquest, I am not sure that it had that much, if any real influence concerning Luther’s reach and the fact that he and others at the time formed a counter influence to the Church. It may be a bit “chicken and egg” to sort out how much influence the spread of Protestantism was due to theological differences, and how much due to the use of Protestantism by civil authorities to rid themselves of Church control or perceived control.
Matthew Komescher in his Catholicism Tody gives part of a chapter to this, and I came across another source which at the moment escapes me; but neither made mention of Islam as it relates to Protestantism.
Hope that helps.
Then, again, I am no historian. I would be interested in what you find.