Hi from an Australian Muslim convert.
Yes, Muslims living in Australia follow Sharia Law. In fact, basically all Muslims (everywhere) follow Sharia Law. Analogously, Christians (everywhere) follow the rules stipulated in the Bible (the Christian equivalent of Sharia Law).
What is Sharia Law?
There's a lot of confusion in Australia about what Sharia Law actually means: see my answer to What is Sharia Law? for a simple description.
Often when Australian politicians talk about Sharia Law, they're alluding to executions, floggings, hands being cut off, etc.; basically corporal and capital punishment. I expect these are considered the "extreme tenets" of Islam, along with jihad perhaps.
Sharia punishments like these need to go through Sharia courts and Sharia judges (qadi); in Australia, we don't have Sharia courts. We can expect to be punished in the afterlife for violating Sharia Law (and possibly in a civil court, if we violate Australian Law).
Muslims are required to obey the law of the land:
Muslims are generally obliged to abide by the laws of the land and the country they live in, whether it is a Islamic state (al-khilafa), Muslim countries, or non-Muslim countries such as those in the west, as long as they are not ordered to practice something that is against Shariah.
The lesser jihad involves fighting back against those who are fighting Islam (Islam Q&A).
To Muslims, the bulk of Sharia Law applies for everyday things: we don't eat pork, women wear hijab, praying five times a day, we don't drink alcohol, we pray five times a day, we don't commit crimes, we give to charity, we eat halal food, and so on. It's all legal in Australia, but it's not newsworthy.
(And, with this understanding, it's strange to ask if Muslims follow Sharia Law: of course they do. It's like asking a Christian if they follow the Bible. It's also why you get Yassmin Abdel-Magied asking Jacqui Lambie Do you know what Sharia Law is? on Q&A.)
In response to:
Basically, do some Muslims choose to follow certain tenets, and ignore other tenets?
Well, yes. Muslims are not perfect.
However, Muslims can choose to follow Sharia Law and simultaneously adhere Australian Law. I'm not aware of any Australian Law which prevents Muslims from following Sharia Law correctly, and it'd probably be unconstitutional to introduce such a law:
The Commonwealth shall not make any law for establishing any religion, or for imposing any religious observance, or for prohibiting the free exercise of any religion, and no religious test shall be required as a qualification for any office or public trust under the Commonwealth.
Section 116 of the Constitution of Australia, Wikipedia
However, if such laws did exist, we are instructed by the Qur'an (and hence by Sharia Law) to simply go somewhere else (Was not the earth of Allah spacious [enough] for you to emigrate therein? Qur'an 4:97). A related question is What should I do if Canadian law and Sharia law are incompatible?
What does Sharia Law in Australia look like?
Let me give some examples how following Sharia Law (in Australia) affects me personally:
- I don't drink alcohol, nor go to bars.
- I wear hijab.
- I pay zakat (charity).
- I moved my money to a bank account without interest.
- I moved my superannuation to Crescent Wealth.
- I pray.
- I only eat halal food.
- (And many more things I forgot to list.)
Violating one of these would violate Sharia Law, and if I'm not granted forgiveness from Allah, I would expect to be punished in the afterlife. I do this only because it says to in the Qur'an (i.e., because of Sharia Law). This is what everyday Muslims essentially mean when they say they follow Sharia Law.
Some other aspects of Sharia Law in Australia:
When we need a ruling, we can ask an imam or a scholar (or Google it); it's not legally binding. This is how Sharia Law is implemented in Australia: punishments for violating Sharia Law (if required) are administered by Allah in the afterlife.
Islamic marriages are performed in Australia in accordance with both Sharia Law and Australian Law (which restricts the age of marriage and prohibits polygamy).
There are mosques scattered around; when I'm in Melbourne, I go to the Emir Sultan Mosque. There's some Islamic schools in Australia, such as Werribee College.
In answer to:
Would "reject[ing] sharia law full stop" equate to abandoning Islam?
It's classed as Kufr ul-Istibdal (Disbelief because of trying to substitute Allah's Laws); see SunnahOnline.com (adapted from Tafsir Ibn Kathir). Rejecting the entirety of Sharia Law would be rejecting a huge amount of the Qur'an.