Really? Mind sharing historical proof to support this?
The only cases of conversion between close churches are also relatively modern, being the great schisms in Catholicism. But I wouldn't consider that to be actual conversions from one church to another, rather a gradual split from one main church into many.
If it was so easy to convert among similar faiths, why then are there so few Catholics in abrahamic Israel, and so many in then polytheistic Rome/Europe? Why did christianism grow faster in polytheistic lands than in monotheistic ones?
Until the Romans got involved, Christianity's proportional make up had a high percentage of Jews, after all it was a Jewish sect for many years. Until the 4th century when the pretty exceptional event of being declared the state religion of Rome, replacing all others its main growth was not in Europe, but Syria, Egypt and the surrounding areas.
It also converted significant numbers of Zoroastrians in the early years, and it is from that tradition that concepts like angels were introduced into the Christian faith, Gnostic's were also common converts.
Even after the Roman conversion, it was centuries of work converting most of Europe. As with all things religion, look not always to reasons of faith and similarity for why conversion was quick or slow, but also to politics. The Orthodox Church for example was able to make inroads into Eastern Europe primarily based on their willingness to provide the liturgy in the native language of the people, while the Roman Church insisted on Latin.
When Islam first made its way to Africa many of the inroads Christianity had made were destroyed, and the native Christians converted to Islam. Egypt for example when from a mostly Christian nation under the Coptic Orthodox Church of Alexandria to a majority Islamic country by the 12th century.
