original post notes that a sign was posted about a change/variance to the rules.

If that is handled the same there as it is here there would have been a meeting for the church to bring up any objections.
that is what the sign is for to let others know about the variance to the rule so they can out forth their concerns.
So any other neighbour would have the chance to attend the meeting and put forth their ideas/concerns for the committee to consider in their decision making 

So original post indicates the committee allowed the change to allow the restaurant to serve the beer.

Then the politicians who had appointed the members of the committee (if it is done like it is here) decided to over rue their committee and cancel the change the committee had agreed to.

Now the committee has been compromised in its decision making and if I was a member would have to consider if I wished to remain or hand in my resignation.