From what I've read, Tavener is a "perennialist" (or something like that anyway). That philosphy holds that all the major "mystical" traditions stem from truth, and are true. But within each are "demoninations" for lack of a better word which are false and heretical. So, for example, Hinduism, Chinese religions, Islam, Judaism, and Christianity are all true. But within Christianity, Protestantism and Catholicism are heretical, and Orthodoxy is true, because Orthodoxy is "mystical" and the others aren't. The same process of distinction applies to the other religions. Try looking up Frithjof Schuon and Ananda Coomaraswamy, who wrote about this.
Tavener's falling out with his spiritual mother was not due to his dabbling with Islam per se, but according to what I've heard, because he began to espouse this teaching even after being warned by her several times, and in the end she told him that the Church considered him a heretic and she had to cut off the relationship.