Prima facie, it'd seem that the common factor enabling their persecution is Islam.
[0]: https://www.theguardian.com/uk-news/2016/aug/09/tanveer-ahme...
Islam does have a huge internal debate over which branch is correct that has never been settled. To not accept this group of people is unique in Islamic countries because they have been using this as a weapon against minorities by creating separate laws. By extending to other muslims this is more about trying to make them lower members of society with less rights and an excuse for mistreatment without breaking religious morals. You are allowed to do things to non muslims that wouldn't be acceptable to a muslims.
Excommunication and intolerance is not at all exclusive to Islam, as the blood-drenched history of the Wars of Religion in Europe demonstrates.
The whole issue seems to be an internal argument among the Muslim community- so Islam is a necessary precondition for this problem, as it's the subject matter of the issue, but not the causative agent.