I don’t think this by-law would stand up to a challenge at the Tribunal. Section 139 says this:
(1) By-law cannot be unjust
A by-law must not be harsh, unconscionable or oppressive. (Note : Any such by-law may be invalidated by the Tribunal (see section 150).
I would be telling the committee that they need to consider the consequences of trying to silence owners who have a right to raise issues with the committee. If people don’t want to communicate with other owners, they shouldn’t be on the committee in the first place.
In the meantime, you could propose an amendment to the motion along the lines of “the strata manager will be required to respond to the owners in a reasonable and meaningful way within five working days or they will be considered to be in breach of their contract.”
That should put the strata cat among the snoozing pigeons.