But government police forces are all working for the same people. These religion-based police forces are definitely not.
Not really.
In Arkansas, the county sheriff is elected - as is the Justice of the Peace, who has limited police powers as well. There are also state police, municipal police, and various state and federal agencies with law enforcement powers. Each of these groups work for different entities, some of which are mutually exclusive.
> These religion-based police forces are definitely not.
A police force operated by a church is no more "religion-based" than the Securitas guy standing outside the grocery store is "retail-based".
If their highest authority is The Constitution and they are trained and act as if it is, then maybe it's OK.
But, this is a church. The church's highest authority is not The Constitution and that immediately calls into question who is the highest authority for any police officer hired and sworn by the church.