There are few categories of exempt employers for FBT.  There are none entirely exempt, there are relevant caps applicable. 

The most common employers are defined as a Public Benevolent Institution (PBI).  A PBI is defined as per the Australian Charities and Not-for-Profit Commission (ACNC).  The employer will also need to apply with the ATO for FBT Exempt status.  The capping threshold for PBI employers is $30,000. This is the grossed up reporting amount.  Essentially this means the first $14,422 - $15,900 (depending on the benefit provided) can be salary sacrificed by employees without any tax consequences.  Any an example of a PBI is a religious institution, i.e. Catholic School. 

The other common employers are Public and Not-for-Profit hospitals (inc Ambulance).  The capping threshold for these employers is $17,000.  Again this is the grossed up reporting amount.  Employees can receive benefits of $8,173 - $9,010 (depending on the benefit provided) without any tax consequences.

This is a basic summary please get in touch if you require further information.