Hi Annie,
In Australia, each of the eight jurisdictions have their own parliaments, making eight sets of laws, PLUS there's the Federal law coming out of Canberra. But all of those 8 jurisdictions restrict access to the bdms for their state/territory. It doesn't matter if they are ordered online or in person, the same restrictions apply. If I want my own birth details, (NSW bdm, registered in rural NSW 1947), I need 100 points of ID before they will consider processing my application. Unless you are named on that document, you have NO chance of obtaining it, until 2047. My younger siblings cannot obtain it, but my older siblings can, for they are named on it. My parents can too, as they are both named on it.
If I consider my 1974 NSW marriage, there's a great deal of sensitive information on it that is simply NOT available for members of the general public to access. The information is not anywhere else on the web. There's no submitted trees online naming my parents or myself or my siblings. Similiarly for my other living relatives who are family history buffs. Nope, trees are not online. My sister in law (the one who is a family history buff) has a tree online... does not include her own generation or her parents generation.
This is not a matter of 'secrecy', it is a matter of respect for the legal expectation of privacy of the individual that has been a tenet of the Australian Democracy for decades and decades, even back into the 1810s when those who had been transported but had served their sentence ie were emancipated, and therefore free, were outnumbering those who were still under sentence.
Back at reply #1 I posted the following link
https://www.oaic.gov.au/resources/agencies-and-organisations/guides/what-is-personal-information.pdf So, in Australia, the concept of privacy of the individual is very different from the UK one.
JM