Please forgive me in advance if this reply gets lengthy. I want to do justice to your very interesting and great question. To answer your initial question regarding what is the relationship between monotheism and reincarnation - there isn't one (a relationship). I will explain further why that is as I continue. No monotheistic religions adopt or accept the belief of reincarnation. There will always be branches of beliefs, that use the mainstream name but "twist" the teachings to suit their own ideas. I am a Christian. Unfortunately, many have given Christianity a bad name because they used the "label" of Christian but their actions showed otherwise (hatred, etc). One thing that must be said here is that God in the Bible actually rebuked religion for not being of Him. Religion is man-made. Christianity is not religion, but rather a relationship and a way of living in love as a result. It is the only monotheistic belief that is not a religion, unless individuals choose to make it into what it wasn't intended to be. Religion is about rules, rituals, condemnation if "XYZ" isn't done, on and on.
Even though my point of view is coming from that of a Christian belief, I do have a good deal of knowledge concerning other monotheistic religions. So my explanation will be Christian, but the same principles apply to the other belief systems that are monotheistic when it comes to reincarnation, only substituting Jesus Christ with Allah, etc. So with that being said, the reason reincarnation and monotheistic beliefs are not compatible is because of the very foundation of what reincarnation believes. Reincarnation at its true core is all about needing to go through these cycles of life "graduating each time" until "you get it right" and at that point, earn the right of salvation/God. Whereas in monotheistic beliefs, "God is the savior." Now - this is where another difference between Christianity and other monotheistic faiths are extremely different. In Christianity, it is not about works that we do to achieve a status with "God." Christianity is the only belief where it specifically says there are no amount of good works you could possibly do to reach salvation. That's why Jesus, sinless and blameless, offered Himself up a living sacrifice on the cross to take our place for our sins, so that we could be seen as holy, spotless before God. It was a gift given freely to us, with no qualification needed, except to say "Yes, I receive." It is/was redemption by God that loves us each unconditionally. It also begs the question: Which is best? To accept a freely given gift of salvation already completed for us? Or living a countless number of lives until you reach a certain level? To back this up (also related to the subject of reincarnation), is when Jesus said: “I am the way and the truth and the life. No one comes to the Father except through Me (Jesus)." So if it were indeed possible to live a cycle of lives to eventually achieve salvation, this would have been said rather than what was quoted. There is also one regarding "good deeds" (which is reincarnation - keep going until you are "good enough") that says: And God raised us up with Christ and seated us with him in the heavenly realms in Christ Jesus, in order that in the coming ages he might show the incomparable riches of his grace, expressed in his kindness to us in Christ Jesus. For it is by grace you have been saved, through faith –and this is not from yourselves, it is the gift of God–not by works, so that no one can boast.For we are God’s handiwork, work of art, created in Christ Jesus to do good works, which God prepared in advance for us to do (after salvation - to extend that love to others)." On the cross, Jesus said, "It is finished" meaning our sins have been atoned for, which is the polar opposite of what reincarnation stands for.
The idea of reincarnation, that people must go through a series of lives to atone for their sins, is a denial of the work of Christ, accomplished on the cross. Salvation has been made complete by Christ's sacrifice. There is nothing (no works) any of us can do to add or subtract from it. Consequently, there is no need for a series of births to accomplish what Christ has already completed. In other monotheistic beliefs, this is the same basic truth but "good works," rituals or some type of acts are necessary to achieve salvation, versus good works being a product of a loving heart after receiving salvation. So in a nutshell, any belief system that is monotheistic, believing and praying to one God, trusts/knows their salvation comes from their God - rather than many lives, almost like "Groundhog Day" spent trying to reach that "status."
I do want to emphasize that I don't judge anyone for having free will to choose what they believe. This is simply what I believe and live and have seen unbelievable miracles happen right in front of my eyes. But I certainly respect everyone and don't ever want anything I say to be perceived otherwise. Hope this answers the question and makes sense
