In Origen's case, they used his wording to justify attacks on his supporters - Origen's supposed crime was saying that there was ever a time that Jesus didn't exist, but it's more complicated and I'm honestly a little confused about what was being said and what the issue was. But that was the big crime, which was used to vilify Origen's other teachings, which included reincarnation. In, iirc, year 545 Justinian (totally winging it, this could be so off) decreed that belief in reincarnation was a crime, and had his army murder Christians who believed in reincarnation.