A lot of people tend to say that the Council of Nicea in 325 outlawed belief in reincarnation so the bishops could control people. If you only have one life then they can control you.
This is incorrect for two reasons. First, reincarnation was not discussed at the Council of Nicea. The closest thing to reincarnation was the pre-existence of the soul, and that was declared anathema in 553 at the Second Ecumenical Council of Constantinople. That would rule out reincarnation by extension, but reincarnation itself was not mentioned there either.
A number of heavy hitters within the early church did oppose the idea of reincarnation, and the general push seems to have come from Irenaeus who lived in the second century. Irenaeus lived during a time when Rome regularly, and often brutally, persecuted Christians. He found himself in charge of a sizable Christian community basically because all the people above him in the area had been killed. There was a lot of confusion and discord within the community, so he thought that if Christianity was to survive there needed to be unity of belief. There had to be one catholic (meaning universal) church.
So Irenaeus went around condemning people he saw as heretics. But he didn't do it out of desire for political power. Partly it was driven by fear. If Christians can't agree on anything then the whole movement might vanish in the face of Roman persecution. Another driving force behind his condemnation was because there really were a whole lot of fruitcakes out there. There were people trying to establish cults of personality, who preached that they could give you all the power of prophecy and unless every person was a prophet then you weren't really born again. You don't even have to think about it to see that this is insane. People take some initiation by a charismatic and then they get up on stage and start spouting whatever nonsense comes to mind as if it were genuine prophecy. Irenaeus did believe in genuine prophecy. He himself had had veridical visions (the death of his teacher Polycarp being one such vision). But there is no way to approach this idea that everyone gets to be a prophet in a rational way. You can't possibly test it. If everyone is a prophet then someone with impure motives can lead a whole lot of weak minded people astray. Irenaeus said that prophecy should be checked against what is written in the gospels (and you need to know which gospels are real in order to check, and Irenaeus was a driving force behind the establishment of the four canonical gospels as canon).
A spiritual successor of Irenaeus, Athanasius, was one of the chief opponents of Arius, whose beliefs were denounced at Nicea. Arius believed Christ was created by God and that the Holy Spirit wasn't even part of God at all. Athanasius was by no means popular. He was exiled several times but he kept managing to worm his way back into his old position as Bishop of Alexandria. I wouldn't say he had political motives, he probably was genuine in his beliefs.
Neither did Constantine himself have any political motives. He too was genuine in his beliefs, and he was a very simple man who wanted to keep everything simple. He convened the Council at Nicea to work out the basics that every Christian should believe, sort of to set out a definition, but he also believed that there was room for congenial debate and disagreement on particulars. He wasn't trying to beat anyone over the head with doctrine. There were times when the bishops were carrying on and he had to step in to resolve issues just to keep the council moving, but it wasn't out of any particular political agenda.
We then move on to the council in 553 and the rejection of Origenism. I don't see this as a power play either. Origen taught, like Arius, that Christ is less than God and is of a different substance than God. What he believed in regard to reincarnation specifically seems to depend on who you ask (and the agenda of who you ask). He believed in the pre-existence of the soul, definitely. All souls were created, not at conception out of nothing as if sperm and egg have magic powers, but by God prior to the creation of the universe. All souls started out as perfectly good, but they have free will, so some of them got bored of contemplating God all the time and they rebelled. When Origen talks about bad deeds souls did in their previous lives he seems to be talking about what souls did in Heaven prior to birth in a human body, not successive human lives on Earth. He also taught that all souls will eventually return to their primordial state of purity, so Hell is not eternal, even if it lasts a really long time.
The problem is that Origen wrote such a vast library of work that it's practically impossible for any one person to read, let alone comprehend, all of it. Whether he believed in reincarnation as such is not important, to me at least, because rejection of pre-existence of the soul automatically rules out reincarnation.
This is all just a side note, however, because the primary goal of the 553 council was the rejection of Nestorianism, which is an entirely different issue unto itself. Origen was just sort of tacked on as a rider. If there were political motivations at the council they weren't the bishop's motivations, they were the motivations of the Emperor Justinian himself. The "Church Fathers," or whoever, weren't trying to control people's lives, it was Justinian. Justinian was a despot and a tyrant and he believed himself to be the world's one true authority on absolutely everything. Anyone who disagreed with him on anything had to face his wrath. If anyone wanted to control a person's one and only life it was Justinian, not anyone within the church, but even Justinian's grip on power could not last forever, and bickering over minor issues would continue. (For example, the Cathars in the 13th and 14th
centuries believed in reincarnation, and they were pretty popular in
what is now southern France, until the king of France had them killed
for political reasons.)
Aside from the no pre-existence thing, I don't really see the control issue entering in. Most theologians just believed that the soul was created either by God at conception or somehow the soul was created by the union of sperm and egg (creationism and traducianism). However prevalent belief in reincarnation was for early Christians, it just seems to have died out by inertia. Theologians accepted the ruling against pre-existence, so they just didn't question it. Not questioning things is something adults do as a matter of being adults, that has nothing to do with trying to impose a power structure from the top down, it's about fitting into a power structure from the bottom up out of pressure for acceptance. People want to fit in. "If my teacher doesn't believe in reincarnation, then neither will I. Please like me." You have a handful of unpopular people with an unpopular idea, and over time there are fewer and fewer supporters until there are none left. That's just how things work.