Hi K,
Interesting, intelligent and pertinent.
I also want to share some thoughts in this context those I discussed somewhere else.
I feel that you missed Judaism as it is also at the same page.
To answer your question, we have to look at the spread of all three religions. All three of them accept that they are originated from Abraham. Judaism spiritual spread ends at Prophet Solomon as after him it did not able to add anything significant, both geographically and spiritually. The reason behind it is believed the curse of God to Solomon.
There are only two Apostles in Judaism which was endowed by a book from the God; Moses and David. Prophet Moses is a central figure and in Judaism. Christianity is for sure started as a vertical of Judaism. Although it accepts prophets and books mentioned in Judaism but the prominent figure here is Jesus Christ. It holds Bible above all previous religious texts. Islam takes the baton from here on. It considers all the prophets and mentioned both in other two religions as its own but declares Prophet Mohammad as a final authority and so the status of his book bestowed upon him.
There is a very important fact about Quran, which is not properly acknowledged.
Although Quran considers Prophet Mohammad as the last one, but Moses is the most mentioned prophet in it; even more than Mohammad. Considering the fact that Quran is bestowed upon Mohammed, it looks a bit contradictory. If we look at the Bible in this context, then we can clearly feel and difference. Furthermore, Quran says that Moses used to visit to God many times on the hill (though in the veil) while Mohammad visited God only once in his lifetime when Angel Gabriel took him across seven skies. Quran says that Muslims should believe in all prophets but did not name any of them except Moses declaring him as a chosen one. So, we see that Islam places Moses almost in the same league of Mohammad. There is absolutely no attempt in Quran to mitigate the status of Moses.
Judaism does not accept prophets and books of other two. Christianity accepts prophets and books of Judaism but not of Islam. Islam accepts prophets and the books of both.
Now we can see that there is clear-cut pattern- The prequel is not accepting the sequel while sequel is accepting the prequel.
Having said that, by no means, I am not trying to hold that the Islamic version of books of Moses, David and Jesus should be considered the real ones. Those may be or maybe not. In my opinion, they are at the equal footings and one should adhere to anyone according to his belief and roots. But, to discuss finer points, we should consider Islam as representative of other two as well.
There is one more reason of it. The literature in Islam is enormous comparing to other two. I feel that it comes second only to Hindu mythologies. The huge population following those two mythologies may also be a reason behind it. Some may disagree but we must acknowledge the fact that a good chunk of their literature is still to be translated in English so it unavailable for others.
Now, coming to your particular point, I do not see any difference between adherance to any one othese three religions.If we see objectively,then is clear that the real adherance is with Prophet Abraham. Thus, it is applicable to all of them.
But, most will disagree with me.
with love,
sanjay