Investigators with the Australian Federal Police said they received a report about the offensive emails in May.
Three emails were allegedly linked to a 59-year-old man.
On Thursday, a search warrant was executed in Woodburn, on the NSW far north coast, with investigators seizing electronic devices and two prohibited weapons.
Right-wing literature and pamphlets and instructions on making explosives were also seized for further examination.
The man has been charged with four counts of using a carriage service to menace, harass or cause offence, one count of intimidating a witness and two counts of possessing a prohibited weapon.
He was scheduled to appear before the NSW Bail Division Courts on Thursday.
He faces a maximum penalty of 10 years' imprisonment if convicted.
AFP Assistant Commissioner Counter Terrorism Peter Crozier said online criminal threats had real-life consequences, including jail time.
"The royal commission was established in response to acts of hatred and intolerance directed at members of our community," he said in a statement on Thursday.
"Any continued intimidation or incitement of violence against individuals who are providing evidence to this inquiry is wholly intolerable."
In October, AFP Commissioner Krissy Barrett announced new National Security Investigations teams to target groups and individuals causing harm to Australia's social cohesion.
Prime Minister Anthony Albanese announced the Royal Commission on Antisemitism and Social Cohesion in January following political pressure, after initially rejecting calls for the inquiry.
The royal commission has been examining what police and intelligence agencies knew in the lead-up to the terror attack at Bondi on December 14.
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