Steven Adam Blackwood, 28, and Stephen Craig Mettleton, 34, spoke only to confirm their names and that they understood the charges against them.
A PSNI officer described them as "foot soldiers of the south east Antrim UDA".
They were arrested on Thursday over the disorder, in which up to 100 people took part.
Both accused are from Greenisland, County Antrim, - Mr Mettleton, with an address at Rossmore Green and  Mr Blackwood of Moyard Gardens.
The police officer said the men's DNA was found on a balaclava and gloves found in a bin near a house in Knockdhu Park, one of three homes badly damaged on 30 March.
A defence lawyer told the court his clients strenuously denied any connection with the UDA.
A detective constable said 29 people have been arrested in connection with the events and around 1000 exhibits had been amassed in the ongoing investigation.
He said that following the incident, police discovered hammers, machetes, knifes and clothing on arterial routes out of Larne.
The police officer objected to a bail application on the grounds of possible reoffending or the intimidation of witnesses.
He said "intimidation is at the core of the UDA".
A defence lawyer said he accepted that the forensic evidence meant his clients had a case to answer, but said he could see no case for remanding them and that strict bail conditions would be sufficient.
However, the district judge refused bail and remanded them in custody.
They are due to appear again 17 July.
Two men have been charged with attempted murder in relation to disturbances in Larne, County Antrim, on Sunday 30 March.