This raises two questions. First, can someone be both a Christian and a Muslim? I would argue that the answer is no. The Anglican church, while not as rigid in doctrine as the Catholic Church, does include the Nicene Creed in the Book of Common Prayer. As an Anglican you believe:
And in one Lord Jesus Christ,
the only-begotten Son of
begotten of his Father before all worlds,
You also believe:
and the third day he rose again
according to the Scriptures,and ascended into heaven,
and sitteth on the right hand of the Father.
And he shall come again with glory
to judge both the quick and the dead:
whose kingdom shall have no end.
Islam believes that Jesus, while a great prophet, was human and that he either did not die on the cross or was rescued from the Crucifixion. The one belief necessarily excludes the other.
Rev. Redding also states that she does not believe in the Trinity as a literal concept and seems to struggle with the divinity of Christ. This would make Rev. Redding an Arian, as opposed to Orthodox.
The second issue though goes to why Rev. Redding felt drawn to Islam. Mostly, it was an question of spiritual yearning. Many western Churches, not just the Anglicans, have moved away from traditional forms of worship, trying to make worship more "relevant" to the times. The Anchoress correctly notes that Western Churches had special services which addressed that those spiritual yearnings, and that those services are being shunted away. I myself am a child of Vatican II, yet I find sometimes the need to attend the Latin Mass occasionally.
The Anglicans especially where in a good position to address those needs. Unlike the Catholic Church, the Anglicans have 450+ years of experience with Liturgical English. I one attended a wedding in an high Anglican church and wondered my we Catholics cannot expropriate more of that language for ourselves. The best English language hymns tend to be those originally written for the Anglican church.
By looking to create a "relevant" church for modern times the yearnings of the faithful are not being satisfied. I think we have all found ourselves in the same place as Rev. Redding occasionally. And considering the power of Islamic belief, I can understand why she looked there to answer her yearnings. I just cannot see how you can reconcile belief in one with the other.