As an Australian who has just endured a Prime Ministership of a member of Hillsong I think it's worth reflecting on what separation of church and state might mean.
Christians have every right to be constituents and thus politicians also have a right to consult with them. However, politicians seeking guidance from the institution of the church, for example, this is what the Pope wants me to do, regardless of the wishes of the constituents, is another matter.
Or Brian Houston. Our former PM deferring to Houston on the basis of shared faith is different to Houston being one voice amongst constituents. The separation of church and state is thus an understanding that politicians can be "corrupted" from their professed role by undue influence. That's a good thing. However, such corruption can come from other quarters, particularly in a corporatoracy, and this is a much greater threat to democracy in our current age.
It's also easy to make the line between constituent and institution look very fuzzy.