Cllr Kim Ashton and Cllr Sean McPeake spoke at a recent meeting about the group.
A unionist councillor has said a Council working group set up to promote good relations is now only being attended by one side of the community.
Mid Ulster District Council set up the Corporate Good Relations Working Group (CGRWG) to assist in policy development and promote good relations.
However, minutes of the group's meeting on March 9 revealed that no unionist councillors were currently attending meetings
Cllr Kim Ashton, of the DUP, confirmed at last week's Policy and Resources Committee meeting that unionists were no longer engaging.
“Just to note obviously now that the make-up of the Good Relations now is really the 'nationalist relations' working group. There is no unionist now attending that,” she said.
“Our party's objection is the amount of money now being spent through this channel looking at a united Ireland.”
Cllr Ashton was referring to a decision taken by CGRWG the to spend £16,000 on a series of workshops discussing constitutional change in Ireland.
The fee will cover management fee, speaker costs, marketing, and digital set up, and the decision was at the time challenged by unionist councillors.
In January 2022, UUP councillor Walter Cuddy said the group was of 'no benefit' to unionists.
“We don't go to the Good Relations Committee because it is of no benefit to us at all. The report says it's been agreed by the GRC that we do this, that and the other,” he said.
“If they come back and say we're better off staying in the UK, we'll never hear of it. This is why we have no confidence in that committee,” he added.
At last week's meeting, Sinn Féin councillor Sean McPeake appealed for unionists to reconsider their opposition to the group.
Afterwards, he added that the 'boycotting' of the CGRWG was 'disappointing and deeply regrettable'.
“In developing Council policies on matters such as Minority Language provision, Council's approach to bonfires and the Removal of Hate Expression policies, Mid Ulster Council always prides itself in following expert and best practice advice, be that advice international or local.
"The Equality and Good Relations sub-committee examines these details and engages with a wide range of experts in the fields of equality and good relations before deciding upon new policies.
“Council has quite rightly been commended by experts in the field of equality as a public body adhering to best practice measures in policy development.
“It says more about the state of unionism in general that they refuse to engage within these processes, processes that are designed to protect minority right for everyone,” he added.
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