To be quite honest, it's not really accurate to say that Protestants were moving away from stricter, more fundamentalist ideologies. Ideas adopted by some Protestant sects included things like Biblical infallibility (vs the Catholic doctrine that everything in the Bible for the purpose of salvation, was true, but its history or science might be wrong), electionism (God chooses who will be a Christian) vs the works of Catholic philosophers like Erasmus who argued that God gave people free will, iconoclism, anti-Saint worship, etc. It's important to remember that many Protestant theologians saw themselves as restoring the original, true, fundamental, and in some ways stricter version of Christianity (in other ways, less strict, and this is also depends on which theologian you're looking at). In fact, the word "Fundamentalism" was coined by 19th century Protestant theologians to describe themselves.

If I had to compare one movement to the Protestant reformation, I'd compare it to Salafism; a reform movement started in the 19th century, aiming to restore "original" Islam, eradicate worship of saints, promote a "literal"* view of the Qu'ran, etc. You may have heard of it, as it has influenced Jihadist thought in the modern era. Most Salafists are not Jihadists, as most Salafists focus on influencing ordinary Muslims rather than politics, but some do, and a small portion of those aim to enforce their version of Islam on other Muslims by force.

*I wouldn't personally describe it as a literal view of the Qu'ran, and I think doing so plays into the hands of extremists, but that's what they claim to be doing.

Still, there is a key reason why Islam didn't have the same kind of radical and wide-spread change in the early modern period as Catholicism. The Catholic church was a rival power to that of the state, and as states became more powerful, they wished to free themselves from the power of the Church. Protestantism was a useful tool for rulers like Henry VIII, even if they didn't care that much about the theology. In the Middle East, Islam was mixed in with the government and Caliph, so rulers didn't want a "reformation". This is the same reason that Orthodox Christianity didn't have a Protesant-style reformation like Catholic Christianity, as Orthodox priests were much more under the control of the state.