It's by a 3-3 split that the High Court decided that these are correct statements of law. (Though Heydon J, in his now-characteristic contrarian fashion, was really seizing on the opportunity to take a swipe at the defects of Lange.) The High Court ordered the appeals of the two men convicted of this behaviour dismissed.
At issue in Monis v The Queen  HCA 4 was the validity of s 471.12 of the Criminal Code. That states:
471.12 Using a postal or similar service to menace, harass or cause offence
A person is guilty of an offence if:
(a) the person uses a postal or similar service; and
(b) the person does so in a way (whether by the method of use or the content of a communication, or both) that reasonable persons would regard as being, in all the circumstances, menacing, harassing or offensive.
Penalty: Imprisonment for 2 years.
The two accused were charged under the offensive limb of the section, for sending letters to deceased soldiers' families. That section doesn't have any direct equivalent under State law, though the prohibition of offensive conduct that occurs in public places is fairly common. Offences under s 464.14 are often charged, as alternatives or in combination with stalking charges, where offensive communication occurs over a telephone.
The two men were convicted at trial, and their convictions upheld by the NSW Court of Criminal Appeal.
The appeal to the High Court didn't allege error in their specific cases; ambitiously, it was argued that the offence itself was invalid, for offending the implied constitutional right to political expression, first voiced in Nationwide News Pty Ltd v Wills (1992) 177 CLR 1 and Australian Capital Television Pty Ltd v The Commonwealth (1992) 177 CLR 106.
French CJ noted at :
The now settled questions to be asked when a law is said to have infringed the implied limitation [to impose a burden on the freedom of communication on matters of government or political concern] are:
1. Does the law effectively burden freedom of communication about government or political matters in its terms, operation or effect?
2. If the law effectively burdens that freedom, is the law reasonably appropriate and adapted to serve a legitimate end in a manner which is compatible with the maintenance of the constitutionally prescribed system of representative and responsible government and the procedure prescribed by s 128 of the Constitution for submitting a proposed amendment to the Constitution to the informed decision of the people?
French CJ and Hayne J agreed that s 471.12 did infringe the implied limitation, and that it was not compatible with representative and responsible government. They would have allowed the appeal.
Heydon J went out on his own, severely criticising the implied limitation as 'unsatisfactory' and 'mysterious'. In pointed comments he noted that no attempt was made to argue that the cases establishing the implied limitation were wrong, and ripe for overruling. Clearly, he would relish the chance to deal with that argument. But, he conceded in the absence of overruling the implied limitation cases, the present state of the law required the result found by Hayne J (and also therefore by French CJ), and so he would have allowed the appeal.
On other thing about Heydon J's decision is that, in a nice touch not often able to be displayed in appellate reasons, he poetically acknowledged the strong feelings in the background to this case, and the loss felt by the parents of service members killed on active duty. It bears reading if for no other reading than to remember the human lives affected by the decisions of courts. I suspect Heydon J found no pleasure in reaching the conclusions he did, and was concerned (at the level of human empathy, rather than legal analysis) of their affect on the families who received the impugned letters.
In a joint judgment, Crennan, Kiefel and Bell JJ took the contrary view. They considered that s 471.12 does not impermissibly burden the implied freedom of communication about government or political matters. They considered the appeals should be dismissed, so that the original convictions would stand.
The end result? Three saying the appeal succeeded; three saying the appeal failed. (I have no idea why there were 'only' six justices deciding this case, rather than the usual 5 or 7, which would have at least provided a majority one way or the other.)
Section 23(2)(a) of the Judiciary Act 1903 (Cth) provides that where the High Court is evenly divided in its opinion the lower court's decision is affirmed. The appeal was dismissed, but because of the way that occurred, there is no ratio in this case because there's no majority decision, let alone majority reason for a decision: Re Tyler; Ex Parte Foley (1994) 181 CLR 18. It seems a wasted opportunity when the highest appeal court in the land is unable to provide any authoritative determination of the law, and the resulting decision is authority only for what it decided.