Thousands of people marched along a road bedecked with Irish tricolours from Lifford, Co Donegal, to Strabane on Sunday to remember those who died during the 1981 hunger strikes at the Maze prison.
It was the first time the event, organised by Sinn Fein, had been held in the Co Tyrone town.
But the family of INLA hunger striker Kevin Lynch announced on Saturday they would be boycotting the event.
Family members withdrew following a row with Sinn Fein over the attendance of the Kevin Lynch Memorial Flute Band (KLMFB).
The band said it had been prohibited from attending the commemoration and claimed it had been told it is no longer welcome at any future Sinn Fein events.
In response, the family said it had withdraw all support for the party.
Sinn Fein has come in for heavy criticism over the decision.
A statement posted on Facebook by the band on behalf of the Lynch family has been liked over 500 times, with dozens of people voicing their support for family.
In the statement, the family said it had been “hurt and disgusted” with the actions of Sinn Fein.
Posting on the East Derry Sinn Fein Facebook page, a party spokesperson said: “We hold the Lynch family in the highest esteem and we deeply regret the family’s decision.“This was an issue between the bands association and the Kevin Lynch band.
“Sinn Fein worked to attempt to resolve the issue.”
While the SF statement offered no explanation for the ban, KLMFB said: “One definitive reason issued by the Sinn Fein Irish Republican Bands Association is that they view two Scottish bands as anti-Sinn Fein dissident bands.
herefore we were breaking the federation rules by marching alongside these bands when attending a Wolfe Tone Commemoration and a Hunger Strike Commemoration recently held in Scotland.”
The band said that, as a consequence of Sinn Fein’s decision, the family would no longer vote for the party, and would no longer support any Sinn Fein events or fundraising.
Kevin Lynch’s belongings have been removed from Dungiven Sinn Fein museum, it added.
The family said it had been “truly humbled” by the support it had received.
Lynch, from the village of Park near Dungiven in Co Londonderry, was arrested in December 1976 and charged with a number of offences including conspiracy to steal weapons from security forces.
He received a ten-year sentence in December 1977.
Lynch spent 71 days on hunger strike from May 1981, and died on August 1, 1981.