An interesting review, but I'm not sure I'll bother reading the book -- I just leafed through a copy in my local library.
Firstly, the distinction between "secular" and "secularist" strikes me as specious, especially considering the political undercurrent in Islam.
More important, the first thing I do when I come across any prolegomena for a future moderate Islam is to check the index and look up the word "apostasy."
Aykol's views on the subject are really incoherent. He overlooks the fact that the inclusion of the death penalty in the sharia can be based on a number of graphic punishments meted out to "the infidels" in the Koran, that the Koran itself is rather incoherent (odd, for a book dictated by God, eh?), that any claims in the Koran to any more liberal attitude may well refer to theological controversies within the umma, or the possibility that Mohammed changed his mind, and that the hadith, which he considers "earthly," are necessary for an understanding of the Koran.
In any case any Muslim should be free to leave at any time he wants, and the question of whether Mohammed would have been magnanimous enough to give him permission is irrelevant. This is a matter of natural human rights, not how "liberal" a dark age theocrat might have been.
No moderate Muslim I've ever read dares take this issue head on, for fear of denying that God gave Mohammed orders to conquer Christians and Jews in the first place. Which would, of course, deny the validity of the Koran.
Irshad Manji's "The Trouble with IslamT gives a pretty good view of what genuinely moderate Muslims are thinking -- even though I have some disagreements with her, too -- and she's just been declared an apostate.
Or better yet, if you're an infidel, read "Why I Am Not a Muslim," by Ibn Warraq, or, if you're a moderate Muslim who's starting to get squeamish, read "Infidel," by Ayaan Hirsi Ali. Both are also under death sentences.