within their "religious beliefs" because those things are permissible when the victim is a non-believer and has been given the opportunity to convert;
That is nonsense.
Yes, but that remains what these heretical fundamentalists believe.
There are three so called "book religions", Judaism, Christianity and Islam. Islam honours all those as "believers". Some fanatics in any of those religions might disagree.
Do you realize we agree? Yes, traditional Islam considers Jews and Christians "people of the book", people at different levels of God's revelations depending on what prophet they are following. A string of prophets, Abraham, Moses, Jesus and finally Mohammed. All prophets of the same monotheistic God. However the non-Muslims were not on a par with Muslims, they were merely "protected people". They had to pay a special tax, were not allowed to bear arms, however they were allowed to practice their religion in private, establish their own courts among their people for certain levels of crimes and the Muslim government was completely obligated to protect them as they would a muslim citizen. This changed over time as European power grew, moderates not requiring the tax and recognizing more equality for civil matters.
However as a matter of fact: all those religions pray to the same god. And actually there are a few more religions that pray to that god, eg. the Yazidis.
The "people of the book" concept and certainly the "protected people" status was also extended to Hindus by some rulers/scholars and to Buddhists as well. Although the arguments for the later were a little more complicated.
However Jews and Christians are not necessarily considered "people of the book" by some of the more conservative believers. They require a certain amount of faith and adherence to a person's respective religious laws to be so qualified. And for even more conservative minds a Jew or Christian in Islamic lands not paying the special tax and otherwise behaving under a "protected people" contract were also not considered "people of the book". So yes Jews and Christians can become fair game with respect to be treated as unbelievers. In short, believers must act as believers to some degree, expectations varying.
And of course, the heretical fundamentalist level of expectation is something that has always existed to some degree. Again, Lawrence was specifically warned to travel in native clothing with guards because there were heretics who would kill him for no other reason than being a Christian in Islamic lands, even with the blessing of the Saudi king.
Centuries of central and north african slave trade was founded upon this idea that a non-believer was fair game.
No, it was founded on the fact that Christians payed a fair amount of money for black slaves!
No. Internal slavery predated and coexisted with the North American slave trade. Various African kingdoms had a long tradition of slavery and would participate in the North American trade. This included several Islamic governments. I believe that Lawrence also witnessed some slaves among the Arabian nobles. Admittedly their situation seemed closer to what in North America would have been temporary indentured servitude, so perhaps something was lost in translation. However it remains a fact that slavery in its most brutal and dehumanizing fashion was practiced by some Islamic african governments and that being classified as a "non-believer" made one fair game, a "non-believer" in the eyes of that government to be specific.