White Australia Party Inc, headed by white supremacist Thomas Sewell, launched the legal challenge after a similarly named entity was banned as a hate group on May 16.
Legislation passed weeks after the Bondi massacre allowed Home Affairs Minister Tony Burke to blacklist "White Australia".
The party's lawyers will on Tuesday and Wednesday argue the legislation breached the implied freedom of political communication and Mr Burke adjudicating bans breaches the separation of powers.
They will also argue the Commonwealth does not have the power to ban political parties, citing a major Cold War-era decision by the High Court.
The Commonwealth has argued the party is not a political party but an arm of White Australia, itself a rebranded version of the neo-Nazi group National Socialist Network.
"Forming a political party was a calculated attempt to secure legal protection for members engaging in openly racist and anti-Semitic speech," the Commonwealth says in written submissions.
Constitutional law expert Anne Twomey said both sides had legitimate arguments, but the case was highly complex and fell into a "grey zone".
"All the arguments are difficult," she told AAP.
"It's a really fine decision for the High Court to make."
A White Australia victory in the nation's highest court would raise questions about the strength of the hate speech and vilification laws quickly ushered through parliament in January.
Prime Minister Anthony Albanese in May said the laws would be robust enough to withstand legal challenge.
Professor Twomey said the government's "loose" and rushed laws were designed to pick up people who were yet to commit offences but were deemed dangerous in the wake of increased political polarisation.
But she warned the broad nature of the legislation meant it could be abused by future, potentially ill-intentioned governments.
The definition of hate speech within the laws left ample room for user interpretation, she said.
"Theoretically, (future governments) could use this kind of legislation as a way of preventing opposition," Professor Twomey said.
There has not been a similar case since the 1950s, when the High Court ruled it unconstitutional for then-prime minister Robert Menzies to dissolve the Communist Party of Australia. It was a Cold War ruling that Professor Twomey said shocked the nation.
She said a 2025 case, in which the court upheld Mr Burke's decision to block the visa of far-right commentator Candace Owens, might also set some precedent.
It made clear the laws could only be used to ban people if they had the potential to incite real harm, not just ot hurt someone's feelings, she said.
The hearing will run until Wednesday, with a decision not expected for some weeks.
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