The shared understanding of God is disassociated from the record of how religious leaders act in accordance to their shared core beliefs, on such a large scale that would suggest there was no God at all.
God, as the Abrahamic religions understand him, formed a covenant with Abraham. This suggests they share the same God, yet these religions' historical relationships and questionable leadership tactics are proof enough that God does not exist.
God is not immutable. Religious leaders subvert his will in the aim of greater political power and material wealth.
Religious leaders and this so called "Subversion" are their choices as individual leaders which are fundamentally people still. God is Immutable and also God is able to change any aspect of Creation.Creation is an aspect of God's will or in other words:creation is one of God's artworks painted with the crayons of life and death.
Those religious leaders are not acting in accordance with his teaching, so their words/actions do not reflect God's.