@JonB
Your last point is a good one - all the religions should not be allowed to form lobbies or donate to political causes.
I think perhaps a fair way to do it is to invite an advisor from each religious group, including the various secular humanist, LGBT groups, and form a consultation panel - a think tank, which the government can dip into for ideas or to bounce things off.
Having that many representatives of different groups advising will see a very tolerant, fair and balanced viewpoint through necessity.
They will probably argue intensely each point. In which case, treat them like a jury, they go into the room, they get refreshments, they are presented with the points of the item to think about, and then are allowed to think about it until they reach some sort of consensus statement - more than a simple yes/no, as it may contain better suggestions. Government can rethink, send things back, etc.
The group would be unelected in the general sense, but would contain members put forward by the various groups (which may elect them or chose them internally any way they want).
Give no group priority over any other.
Hmm - perhaps this is one for the halfbakery...