Mason James Robbins, 30, from Perth, was among a group of 17 members of the National Socialist Network who faced charges over the gathering at the South Australian War Memorial.
At his first appearance in court on January 28, Mr Robbins was bailed to seek legal advice on charges of carrying an offensive weapon or article of disguise and using a Nazi symbol or salute.
The charge of displaying a Nazi symbol was linked to the wearing of an arrow cross, which is the group's insignia.
Under new laws introduced in SA in 2024, people found displaying swastikas or Nazi symbols in public or performing a Nazi salute could be fined up to $20,000 or face a year in jail.
But when Mr Robbins reappeared in Adelaide Magistrates Court on Tuesday via phone from Perth, prosecutor Ciara Fanning-Walsh sought leave to withdraw both charges "on information".
The court was not told what the information was that led to the charges being withdrawn.
SA police declined comment to AAP on why the charges were dropped.
Police agreed to pay Mr Robbins' legal costs of $1210.
During the men's initial court appearances, another police prosecutor told the court the NSN was a "right-wing extremist group with national socialist ideology".
"The group aims at preparing for a race war which it believes will usher in a white separatist ethno state," she told the court.
During his first court appearance, Mr Robbins' lawyer said there would be an issue "lurking in the background" about the constitutional protection of the implied freedom of political communication.
"It gives rise to questions about the validity of any law that seeks to prevent contact and communication between members of, if you like, a political party," the lawyer said.
But the prosecutor said the group was "not a political party" and had taken part in a "co-ordinated incident resulting in criminal offences".
An SA man, Shannen Bartel, 24 of Brompton, who was also arrested over the same incident, had his charge of failing to cease loitering withdrawn on March 5, with police also agreeing to pay his legal costs.
The other charged men, from Victoria, NSW, Queensland, WA and Tasmania, are due to reappear in court later in March and in April.
They include the NSN's leader Thomas Sewell, 31, of Wantirna South in Victoria, who has yet to plead to one count of loitering and one count of displaying a Nazi symbol or salute.
He initially refused to be bailed because he did not recognise the authority of SA's courts, but later signed his bail papers and was released.
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