The criticism follows the election of Cathaoirleachs in Offalys three Municipal Districts.
Fianna Fail is "making up the rules as they go along" in Offaly, according to a Fine Gael rep in the county.
Neil Feighery also says he is declining a nomination to serve as Leas Cathaoirleach in Tullamore on a point of principal.
He is criticising Fianna Fáil members over differing positions taken in two different areas when it comes to co-opted representatives seeking leadership roles.
Shane Murray secured the Cathaoirleach chain in Tullamore after being brought in to fill Tony McCormack's vacant seat after his election to the Dail.
However Eleanor Clendennen failed to secure support to assume the role in Birr after Fianna Fail reps in the area indicated they would not support her nomination, she was co-opted onto the council after her brother John won a seat in the general election in 2024.
Councillor Feighery says he had to make a stand:
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