I agree that there is a line of demarcation. But I am arguing that the line is further out than you are saying. I don't think its a slippery slope because we seem to have the line quite well drawn: The Islamic god-concept is considered acceptable by Jewish standards, the Christian one is not. Even more than that - we (OJ's) need to have the line drawn clearly because it has practical ramifications on how we can associate with them.
You are also assuming that differences between sects are minor compared to those between religions. I don't think that's necessarily so.
I am glad we agree there has to be a line of demarcation. Now, the next point is to decide where that line is drawn. You draw the line between Judaism and Christianity, but not between Judaism and Islam. I draw the line between all three.
However, what is notable here that Jews themselves living in the times of Mohammed, drew the line between Judaism and Islam. That is because they knew of Allah's Pagan past, possibly a moon God, hence they did not accept Mohammed's effort to pass of Allah as YHWH. I understand there have been a few later Jewish scholars who have accepted Allah as the Jewish God, but the overall consensus appears to be Jewish people do not accept Allah as their God.
I don't think that makes a difference. First of all, say instead of two daughters, we speak of their children who never met their grandfather. Does that mean daughter Y's kids are going to believe in a grandfather that never existed? Let's say instead of a grandfather it was a teacher. Student A heard X and student B heard Y, but the teacher really said X. Now both students pass on these lessons to their students in the name of their teacher. Doesn't B's students believe in a teacher that never existed? Its the same idea. There's key concepts here that parallel each other enough that we would say, they believe in the same teacher but one of them is mistaken as to what the teacher said.
The problem with your analogy is that we know that people have ancestry, so you have a father, a great grandfather, a great great grandfather, hence if you claim your great grandfather said x but another says he said y, while I can doubt whether he really said x or y, I do not doubt the fact that he existed. On the other hand, God is not a human person, God is an infinite, omniscient, omnipotent spirit. The only way I can know God exists, is from those humans who have claimed to experience him or his messengers. Hence, I know nothing of God beyond the narrator who describes God. However, the trouble is there are many narratives of God. This time I can doubt the narratives and also the very existence of God itself.
Hence, we cannot speak of God as separate from the narrator.
But we can take integrate your idea into this as well. Because the fact is that Muhammad got his god-concept from Moses (or if you prefer the scholarly tradition, from whoever came up with the Jewish version). That is true both from a scholarly point of view (they certainly seemed to have borrowed heavily from the Jewish tradition) and theologically true as I'm fairly sure Muslims validate their religion as a continuation of Judaism through supersessionism.
5. Moses heard it right and Muhammad borrowed from it.
I would argue that Mohammed's God is not God but another image or concept of God. Although you have tried to argue that Mohamed 's God is the same God of the Jews, and I have agreed with you in spirit or character it definitely far closer to the Jewish God than the Christian God, you have failed to answer my objection that if the the Muslim God is the same as the Jewish God, why does the Jewish God love Jewish people and the Muslim God hate Jewish people?
I don't think that would be true even within Judaism. Different prophets have different revelations of G-d. If they all experienced revelation differently than are you going to say that they each had a different god? In Song of Songs 5:10-11, G-d is described as having a ruddy complexion with black hair. In Daniel 7:9 G-d is described as "ancient" with hair like "white wool". Do Solomon and Daniel worship two different gods? Even Adam before he sinned and after he sinned had different revelationary experiences. Does that make him a polytheist?
Have you noted the two descriptions you gave me are opposite? One says "Black hair" and the other "white hair" This can indicate any of the following possibilities
1. God has black hair
2. God has white hair
3. They both experienced two different God one with black and another with white hair
4. They both made it up
5. They both experienced the same God according to their own perceptions
I will discuss (5) with you next.
And we say the opposite. Because we uphold apophatic theology, no image would ever be a valid image to remind one of G-d with any effective degree of legitimacy. Therefore we Jews prohibit all images and only use abstract references.
I don't think you realise according to Hindu understanding anything you attribute to God is an image. An image need not to be visual, it can also be a word-image. We consider your YHWH to be as much an image as Shiva, Vishnu, Divine Mother, Rama, Krishna. That is because you make attributions to it and draw narratives, your God YHWH is a God that is concerned with people in the Middle East, and hence he has little draw for us Indians. On the other hand, our God Vishnu or Shiva is concerned with people in India, and hence has little draw for people in the Middle east. The names we assign are all culturally specific, our names are Sanskrit names and yours are Hebrew/Semetic names. The attributes we assign are also culture specific, our God incarnates to restore dharma; your God intervenes directly or sends messengers.
As soon as you have said anything about God you are giving attributes and narratives and hence that becomes a concept of God, rather than God itself. In Hindu philosophy we understand this, hence why we make a distinction between Nirguna Brahman(God without attributes) and Saguna Brahman(God with attributes) Nirguna Brahman is unknowable through our ordinary senses and mind, because it is beyond sense perception and beyond reason, it cannot be described or fathomed, because as soon as you attempt to do so, it ceases being God. Think of it like the Tao, "The Tao that can be named is not the Tao"
How do we know that there is a God at all if God is unknowable to us using our senses and mind? The answer is we know through both inference and testimony. The inference is very much like a Kantian inference, I know the the noumena(reality in itself) exists, from the fact there is phenomena(reality as it appears) Similarly, we know God exists, because there has to be a substratum for all of existence, from which this proceeds and into which it disappears. This substratum has be also the substratum of all consciousness, from which all souls originate and into which they disappear. This substratum also has to be substratum of all bliss, from which all things derive their bliss. Hence we say God is satchitananda, meaning existence-consciousness-bliss --- or in other words God is BEING.
If you are intellectually inclined, the the above inference will convince you. If you are not, then it simply based on the testimony of Rishis or seers that we believe God exists. However, in Hinduism, which I don't think is present in your religion, we have a way by which we can directly experience God. In other words we can experience what the Rishis experienced. As God is BEING, I am intimately connected to God through my consciousness. Hence, I can directly experience God within my consciousness. What is currently preventing me from experiencing God is my consciousness is directed through the senses and the mind, and knows no other way of knowing reality. I am forced to think in terms of words, objects, categories. I thus withdraw my consciousness from going outwards into the world, to going inwards to the BEING of my SELF. In order to achieve this aim we developed Yoga and meditation whereby we suspend the senses and the mind(Be Still and know that I am God) Thus, we are the only religion that gives you a practical method by which you can experience God yourself.
As consciousness goes inwards towards the SELF or BEING it passes through stages. One of those stages is when you experience a vision(darsana) of your own God concept. So a Muslim will experience their own God concept(Allah) a Taoist theirs(Tao) a Buddhist theirs(Nirvana) a Vaishnava theirs(Vishnu) and this explains why different prophets have different revelations(white hair or black hair)
It is unavoidable that we all have to start with some God concept and hence why in Hinduism a Hindu has freedom to choose whatever God concept appeals to them the most, like Vishnu, Shiva or Divine Mother, or Hanuman, or Ganesha. There are some Hindus that even like the Jesus or Allah god concept. It need not be a personal God though. Other Hindus prefer to use more abstract concepts like God as the "Self" or God as "Primordial Vibration" or God as "Source" Based on your temperament, different concepts will appeal to you. We do not have this "One size fits all" mentality that Abrahamic religions do. In Christianity you can only relate to God as "Father" but what if you feel better relating to God as Mother? In Islam you can only relate to God as Master, but what if you want to relate to God as friend, or guru, or your child? Recognising the differences in peoples preferences and tempers, Hinduism is democratic.
I sense a possible objection that you insist that your God image is not a image but God itself. To that I reply, that is what they all say
It requires humility to accept that God is beyond all sense and reason and therefore cannot be fathomed using our senses and mind.