Auditing and training are not tax free because they claim to be a religion. They are tax free because they are a service and not a retail sale. Again, this is state and local taxes.
Auditing and training are deductible items on an individual's 1040 because they are considered a religious donation. It is not the same thing as being "tax free" from sales taxes.
The FICA rules have been covered AnonMary.
The reason churches are not taxed in America is becuase the First Amendment says "Congress shall make no laws respecting religion." Respecting here means "in regards to," not in the sense of showing deferrential regard.
The Anabaptist Jacques