I am not very well versed in Australian law, but this indicates to me that free speech is indeed protected in Australia.
It aims to, but it is not a right.
See the two exclusions on the page you linked.
blocked when…
( a ) For respect of the rights or reputations of others; ( b ) For the protection of national security or of public order, or of public health or morals.
In this case, public order may be considered valid, although my personal view is that it wasn’t.
In Australia, humour has a long history of bad taste, but a longer history of religious repression through law. Think 1960s America - that describes much of Australian rural culture, with extra bad language. (Although NSW was a lot more tolerant when I travelled around the country)
In the UK, free speech is not possible either. See D-notices, and later super-injunctions to stop media and individuals reporting on facts.