Extract from a local code of conduct complaint in relation to a ward member being perceived by a planning applicant to have not engaged with them:
From Monitoring office - All members are fee to engage with who they wish, or deal with which matters they wish, and in this supporting or objecting or not being involved with the matter.
As a result there is nothing in the law or the Code of Conduct which can compel a member to engage with someone on a matter and whilst the concerns of the Complainant are noted no breach of the Code arises from the complaint.
So it may be seen that not engaging with a particular matter is not a basis for upholding a complaint.
You'd need a stronger case than "...posted to 1 FB page but not another..." to satisfy the "...improperly used their position to confer an advantage or disadvantage on themselves or another..." scenario of the CoC.