According to Australia's 2016 Census data, the Church of Jesus Christ of Latter Day Saints (Mormons) forms 0.3% of the population. Mormons have been more or less invisible on the political landscape. I have been politically active for most of my long life and I can't recall any members of any Australian parliament who were/are Mormons.
I can't even recall them being politically active i.e. active in political campaigns, door knocking, public statements, etc.
Until the last few years.
In recent times, a program has come about called Safe Schools Coalition Australia and http://www.education.vic.gov.au/about/programs/Pages/safeschools.aspx. This program has caused angst and outrage among people on the political right and out of the woodwork has come some people who are Mormons.
These people have found a home and consolation within the right wing of the Liberal Party of Australian (Victorian Division). To clarify the political spectrum in Australia, the Liberal Party in Australia is a party more like the Republicans in the USA and the Conservatives in Britain. There would be some true Liberals in Australia's Liberal Party but there are also Conservatives and people on the Far Right of the political spectrum. So if Mormons joined an Australian political party it is highly unlikely that they would join the Australian Labor Party (which is the equivalent of the USA's Democrats).
In the wake of the scare campaigns run by the Right and the Mormons in relation to the Safe Schools program, Mormons have been acquiring strategic influence in the Victorian Liberal Party - and, in some quarters, this is causing concern.