Does Australia have laws protecting freedom of speech, freedom of religion, etc.?
This is a very complex question. The simple answerer is no, in as much as Australia has no Bill of Rights like in the US. The Australian constitution deals with the processes and institutions of government rather than limitations on governments. It divides duties between states and federal government etc. however, depending on who you talk to, there are some rights implied in the constitution, for example it is argued that the assurance of regular elections is an implication of the freedom of speech and of opinion. Secondly to this there have been subsidiary laws passed such as anti discrimination laws that protect some basic rights. Essentially as you can see there is no body of law that directly deals with the issue of Rights it is a complex field that covers many arias of Australian law and is subject to interpretation.
