wooderson:
Uh, GWB is a Methodist. Specifically, a member of the United Methodist Church, a mainline protestant denomination in the USA.
The leadership of the UMC is rife with theological liberalism, so much so that, the theological conservatives in the UMC are contemplating separation. Many individuals dissatisfied with the drift of the church leave and they are some of the folks swelling the ranks of the conservative churches. This is common across the mainline prot churches that have gone theologically liberal: loss of parishioners to theologically conservative churches.
Also, the UMC is a member of numerous theologically liberal organizations to include the National Council of Churches and the World Council of Churches.
It is thus no surprise that GWB would mouth such language, if one is to equate his theology with that of the UMC's leadership. I am more likely to attribute his ecumenicalism to politics. Either way, it is incorrect.
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As to the Anglicans, you must be more specific. Some of the organizations are theologically liberal and some are not. The leadership of the largest Anglican org in the US is theologically liberal and many Anglican churches have decided to dis-associate themselves from it. They will find their connection to the Archbishop of Canterbury via another route.
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One last thing, evangelicalism and liberal theology are not mutually exclusive concepts. They are different concepts and some manage to square them, though this is a minority of a minority of Christians in the USA.