Sorry, but that argument dies the moment they mandate for all staff, not just customer facing. Which they have.
How do you justify the BHP mandate?
Well this is a thread about QANTAS on a pilot forum so I've given an opinion of what might apply to pilots. So the 'argument' does not change for that set of employees.
You have to remember that this is a test of unfair dismissal rules, we are not discussing murder or theft of property. As no overall rule exists for this then a commissioner has to make a ruling based on what I've discussed before. The company can still mandate such rules until someone enacts laws banning it as has been done in some states in the US. If it's written into contract that workers agree to then that covers it, regardless of rulings. So we have narrowed this down to how can an existing employee be treated if choosing not to vaccinate and the company has given proper notice, warning and time to allow such effect.
The answer partly can be to re-employ such worker in an area not requiring vaccination, if its a company wide mandate this may not be possible. Then it comes back to the question, is it lawful and necessary? Lawful has been discussed under discrimination and rights. So we come to whether it is justified. In the case of non customer facing then it becomes harder, but still possible to claim it's for health and OHS reasons, or even cost of maintaining higher level of cleaning and so on. In the case of BHP they could cite reasoning such as operating in close quarters remote environments, where the risk of infection and transmission balanced against being able to provide adequate medical provisions. In city tower blocks we could see reasoning such as closed environment promoting transmission and transit of vulnerable staff that work in such facilities.
There's a myriad of possibilities based on infinite workplace scenarios, however the case for airlines front facing staff is pretty much in line with what has already been tested.