We can't find a word for it!
There is one word that fits the situation when a councillor is not allowed to speak on a subject because of his/her association with it. We can't think what the word is - it is possibly the opposite to democracy?
A certain councillor was not allowed to speak on spending council tax payers money for a sign denoting another name for an established community centre.
When a councillor cannot speak for the residents he/she represents there is something wrong somewhere!