2.11 You must not use or attempt to use your position as a Member of the Council improperly to confer on or to secure for yourself or any other person an advantage or disadvantage.
2.12 You must when using or authorising the use by others of the resources of the Council:
(i) act in accordance with the reasonable requirements of the Council;
(ii) ensure that such resources are not used improperly for political purposes (including party political purposes); and
(iii) have regard to any statutory or other requirements relating to local authority publicity
2.14 You must give reasons for all decisions in accordance with any statutory requirements and any reasonable additional requirements imposed by the Council.
Is it disrespectful (2.1) to "ban" an individual without a motion of the council following a social media policy?
Is there a social media policy which empowers named individuals as admin for social media? If not, on what authority is a unilateral sanction imposed? Is there a 'discrimination' against a listed category (2.2) - impaired mobility prevented attendance at a council meeting for example? Is it a 'write' only restriction or is it 'read' and 'write?' Is it a 'council' sanction or that of an individual Cllr (2.11)? Is it a 'political' sanction (2.12 (ii))? Has there been a communication of the reason for the decision (2.14)?
That's the CoC elements that may be relevant, there could also be policy in regard to social media.
You'd have some trouble making any of that 'stick' via CoC - probably best to just start your own social media page and post what you want when you want - you can always screen shot the original content and add your own commentary at your own page...