The OP did write:

The history of religions sometimes resembles the history of viruses. Judaism and Islam were both highly virulent when they first broke out, driving the first generations of their people to conquer (Islam) or just slaughter (Judaism) everyone around them for the sin of not being them. They both grew more sedate over time.

Which I think acknowledges some of that early history. I assume what is said about Judaism has to do with the slaughter of Canaanites, which is possibly more than half legendary, unlike the exploits of Islam which happened in a much better documented time.

In different times and places, Islam has been extremely sometimes fanatical, and at other times received Jews who were driven out of Spain by the Inquisition, and showed toleration of other ideas. The ups and downs have probably been due to many causes, but there really has been an awakening in recent decades of Islamic fanaticism, and in this case, at least, I think the OP's thesis might account for some of that; the thinking was just a bit too loose and brainstorm-ey. It is kind of a puzzle to have so many Muslims combining western education, and the ability to function in a modern metropolitan setting combined with extreme fanaticism.

A peak of Christian holy-warring, torturing and witch-burning came when Protestants set out to rid Catholicism of the many "irrational" (having no basis in the bible) false sacraments, and between the Reformation and the Counter-reformation, both Protestants and Catholics were studying the gospels more rigorously and attempting to weave it into a more logical justifiable structure.

I grew up in the 50s and 60s in a very loose sort of Methodist protestantism that was very unconcerned with issues like the literal 7 days of creation, with hell for sinners, with Satan going around tempting people, or with contesting evolution. It seemed to me only a few fossils insisted on all those sorts of things. For most, a general sort of largely "good Samaritan" morality seemed the most salient thing, and there was not much in society to challenge the general sexual mores of moderate protestantism.

I think it's true generally, that religions, especially if lacking a strong central structure like that of Catholicism or Mormonism, or Islam esp. in times when the idea of a a caliph seemed remote, tend to "mellow" most of the time, especially when not particularly challenged, and to evolve into largely going through the motions, but many different things contribute to a stirring of popular zeal and fanaticism. Both being in close contact with challenges from other belief systems and schooling that trains people to be more logical can contribute, and the result can be a lot of ideas that people half-forgot and certainly didn't apply rigorously start to come to the fore.

I have listened on audio to both the Koran and the Bible, and admit that the Koran has a stronger more consistent version of the meme that God loathes unbelievers and intends to torture them for eternity, but it is a part of Christianity too, and in Islam it has frequently faded into the background. Again, Islam having been established last, is intensely aware of Judaism and Christianity, and rants against them specifically, but at times (esp the 16 and 17 centuries) there were more islands of toleration for Jews in the Muslim world than in Christiandom. Constant assertion that Islam is uniquely inhumane are just the sort of thing that strengthens fanaticism. In criticizing religion, I've come to the conclusion that we should tell believers that to the extent they believe in God's loathing and wanting to torture "Infidels", their beliefs present a real problem to others.