At the risk of derailing this thread at the beginning, why only these two faiths, opposed to say Sikhism, Hinduism, Buddhism, or Daoism?

On Islam, one of the arguments made is the Koran itself, which is a remarkable work of literature and expression of the Arabic language. Unfortunately, that kind of argument won't have the same kind of appeal for those who aren't fluent in Arabic, nor for those* who aren't attuned to traditional literature (whose idea of great literature of Harry Potter or Game of Thrones).  A poster who shall remain nameless actually posted a reasonable link on this a while ago. Otherwise, I think the arguments are mostly going to be spiritual and philosophical ones -  Islam is a purely monotheistic, universal faith with what I would say are some noble examples and ideals, whether we are talking morally, spiritually, or mystically. 

I think Judaism would probably have similar appeal (if it does appeal). Judaism (by which I mean Orthodox Judaism - the only type I would consider) is somewhat less open to converts, and, for adult males, conversion is somewhat daunting. This may put off converts (though Judaism doesn't have the same need to proselytise, of course). 

By the way, I haven't read Bill's article, but it seems strange to me the abstract talks about the arguments of C. S. Lewis and T. V. Morris. I'm a great admirer of Lewis, at least, but it seems to me that it, for example, the Greek Fathers would be more important interlocutors to interact with on the incarnation. Maybe he does do that.

* I don't mean you John. I'm talking generally.

I would consider the strongest arguments against Islam and Judaism to stem from what they have in common, that is the Abrahamic and Exodus backstories.
 
First of all the contents of those stories and the notion of a special revelation itself, especially one directed at a specific tribal group, appears incompatible with the nature of God. A lot of the moral claims are unjustified (cf the food taboos) and some the pronouncements verge on blasphemy - example 'I am a jealous God'. As an additional factor these texts show an apparent dirth of material on the soul and the afterlife. I doubt that ancient Judaism was completely materialistic but it does appear to lack a set out transcendent eschatology.
 
As most would accept a lot of the empirical claims made in Genesis e.g. the garden, the Flood, the genealogies, and the Tower of Babel are false. People urge an allegorical interpretation, which is perfectly legitimate, but then again one has to ask 'An allegory of what exactly'? Of human wickedness and the need for the coming Messiah? In that case they cannot serve as justifications for Biblical revelation.
 
Finally the deeper conceptual issue is that the Fall (or Original Sin) plays a role in each of these religions. What earthly reason do we have to accept such a thing – the Eden story is false on empirical grounds and the human capacity for wickedness is explicable in other ways e.g. through epistemic limitation and free will. I suspect it’s also necessarily false as incompatible with God’s nature – why all of humanity be deprived a direct connection with the Deity on the basis of others misdeeds? The Molnist answer is spurious, of course Catholics have a better answer, that is that naturally humanity does not have a capacity for such direct connection and that it was a gratuitous gift to our first ancestors. Again why believe that humanity lacks such a connection – if anything natural theology and the study of mystical experience points strongly in the other direction

DanielCC wrote:

Finally the deeper conceptual issue is that the Fall (or Original Sin) plays a role in each of these religions. What earthly reason do we have to accept such a thing – the Eden story is false on empirical grounds and the human capacity for wickedness is explicable in other ways e.g. through epistemic limitation and free will. I suspect it’s also necessarily false as incompatible with God’s nature – why all of humanity be deprived a direct connection with the Deity on the basis of others misdeeds? The Molnist answer is spurious, of course Catholics have a better answer, that is that naturally humanity does not have a capacity for such direct connection and that it was a gratuitous gift to our first ancestors. Again why believe that humanity lacks such a connection – if anything natural theology and the study of mystical experience points strongly in the other direction

Muslims apparently deny hereditary sin. They think that after Adam and Eve ate of the fruit of knowledge, they repented and sought (and therefore received) Allah's forgiveness. (The way that is phrased might leave open the possibility of hereditary sin, though, if the story happened as Jews and Christians think.)

Which is to say, it isn't really Rabbinic Judaism. Even conservative reformed Judaism is like very liberal, pick-and-mix Protestantism. I'm not the kind of person to put strong emphasis on historicity. I care much more for spirituality, morality, and symbolism. From my perspective, there is no comparison between reform and Orthodox Judaism. It's like comparing Eastern Orthodoxy with a Protestant mega-church. But, still, I think Orthodox Jews can make similar claims to Orthodox and Catholic Christians on the place of tradition in giving us the Scriptures. The Rabbinic tradition does also go back to the Second Temple. The OT itself, in its final form, isn't too much older. Finally, I think it would be a mistake to consider the Rabbinic tradition frozen in time, or inapplicable to enduring issues. What such claims usually mean is that people want to dissent from tradition on modernist principles.