The question has gotten much more airplay around the Red Mass (including the West Wing episode The Red Mass). And Catholicism isn’t anywhere near as close to a State religion in the US, as Anglicanism would have been in Australia before Federation.
Ulysses Elias’ answer points out the wording in the Australian constitution. A church service on Parliament is not
- a law for establishing any religion,
- imposing any religious observance (attendance is not compulsory)
- prohibiting the free exercise of any religion
- a religious test as a qualification for any office or public trust under the Commonwealth.
It is of course not quite the spirit of what we understand by church–state separation; but it does hew to the letter.
Of course, in reality, while any number of Christian sects kinda coexisted in Australia of olden times, there’s a reason St Paul’s Anglican cathedral is on the central crossroads of Melbourne CBD, and St Patrick’s Catholic cathedral is on the boundary of Melbourne and East Melbourne. It’s aligned to the religion of the head of state of Australia, one Betty Windsor, Fidei Defensatrix . The establishment religion of Australia was the establishment religion of England, which is Anglicanism. These days, of course, that is an historical rather than a living fact.