Apparently she has taken her Shahadah, which means two witnesses heard her say, "There is no God but God, and Mohammad is his prophet." It is what a baby hears when born, and what Muslims say daily. She attends the mosque at Seattle. She thinks she can be a Muslim and a Christian at the same time, but her Bishop Geralyn Wolf does not and the notice of inhibition states:
Standing Committee has determined that Dr. Redding abandoned the Communion of the Episcopal Church by formal admission into a religious body not in communion with the Episcopal Church. The bishop has affirmed that determination.
I find it odd that a Christian who might be sympathetic to Islam and its purity of intent would want to join it. The idea that Isa, Jesus, recited the Book that was again corrupted, so that Muhammad then recited it, and it was preserved and was not corrupted, simply flies in the face of any critical understanding of the historical Jesus at all. Whilst, also, it is just possible that this business of too short a time on the cross meant Jesus did not die on the cross (I don't go with this), the idea that Jesus was raised up by God and replaced on the cross is nuts. Even the notion that the Qur'an is perfect in word order and punctuation is something incredible, and not credible to how it was compiled. Given its claim to perfection, the Qur'an contains mistakes and errors that simply shatter such a claim.
In contrast the person of Jesus (regarded as 'the Word' in tradition) is one removed from the New Testament within Christianity (regarded as 'the words'), and the New Testament and its use of the Tanakh can be subjected to a highly critical approach (which moves anyone away from, not towards, the Islamic view, with the expection of the doctrine of the Trinity - which, in its own criticism, the Qur'an misinterprets).
Islam does not intepret Christianity in the manner Christianity understands itself, and Christian views undermine how Islam understands itself as the original revelation and final prophet.
An English priest Rev. David Hart became very involved with Hinduism without renouncing his Christianity. I can understand that, because Hinduism has a flexibility that incorporates the Christian and there are Christian pluralist views about Incarnation and transcendent views about God. There are clearly different religious structures of time and space (e.g. linear Christianity and incarnation, spiral Hinduism and manifestation) but there are also overlaps. There are also overlaps and interlockings between Christianity and Buddhism (which I share myself - though this alters both), though mainly individuals choose to follow one or the other in terms of practice and outlook (I used to receive Faith and Freedom when the then Anglican book reviewer became a Buddhist, and she quickly acquired the complex language of that faith and reviewed Buddhist material accordingly).
Islam is quite singular and clear and purist, and I cannot see how an individual can mix and match between them. Each might offer the other insights, but Islam is quite thoroughgoing for it to be Islam and many of the Islamic insights are present within aspects of Christianity already.
However, Rev. Ann Redding is to be removed from post not because she has Islamic sympathies but because she has joined a different group. Bishop Robert Duncan, formerly of the Diocese of Pittsburgh, was not removed for his orthodoxy, but because he was setting up to leave, and was having it both ways, and they have both been treated in much the same way.