There is a lot of information about FBT exemption for religious institutions such as churches. But I can't find any information on the history of this or the reasons for the exemption
Come on, you can't just assume that everybody knows what you are talking about. You have to explain your question well enough that someone can look up an answer.
What is FBT?
What country are you concerned about?
Do you know any reason why "religious institutions" and "churches" should or should not be exempt?
Are you aware that "religious institutions" and "churches" might be different things?
In the USA the constitution says "no religious Test shall ever be required as a Qualification to any Office or public Trust under the United States" and "Congress shall make no law respecting an establishment of religion, or prohibiting the free exercise thereof". This has been variously restated, and nobody knows for sure what it means, or even what it says in some cases. For instance, it does not apply to incorporated churches. Those exist under the Internal Revenue Code section 501C3 and are subject to anything Congress wants to do to them. Unincorporated churches are a different being, and very few people know that, even among church leaders.