The ATO has clarified a number of issues around FBT and taxi travel.
 

For businesses, taxi travel by an employee is an exempt benefit if the travel is a single trip beginning or ending at the employee's place of work. The ATO says taxi travel can also be an exempt benefit if it is a result of sickness or injury and the whole or part of the journey is directly between:

  • the employee's place of work; 
  • the employee's place of residence; 
  • any other place that it is necessary, or appropriate, for the employee to go as a result of the sickness or injury. 

For Not-For-Profits, depending on the type of NFP organisation, certain benefits they provide to employees may receive concessional treatment from FBT. However, some benefits may be exempt from FBT altogether. For example, taxi travel by an employee is an exempt benefit if it's a single trip that begins or ends at the employee's place of work. It will also be exempt if it's the result of sickness or injury, as above.

The exemptions for businesses and NFPs are limited to travel undertaken in a vehicle that is licensed to operate as a taxi by the relevant State or Territory. The ATO says they do not extend to travel undertaken in a ride-sourcing vehicle or other vehicle for hire that do not hold such a licence.

Source: https://www.ato.gov.au/Business/Business-bulletins-newsroom/Employer-information/FBT-and-taxi-travel/