If a Christian Arab uses the term Allah, he's thinking of the same God as other Christians, in other words, the God who is a Father with a Son, and ONLY the Father who has a Son named Jesus. The god the Muslims worship, Allah, has no son, and according to their god's book, and so, according to Muslim belief, Allah says Jesus is merely a prophet and not his son. It's not just a matter of them not knowing of the Son, it is a matter of their deliberate worship of a god who has no son, no messiah. Clearly then, they worship something different, though they have appropriated the same names and their terminology may descend from both Christian and Jewish sources.
For example, if I said I am interested in cardinals, one group of people might assume I am a bird lover.
Another might assume I am a St. Louis baseball fan.
Yet another might assume I am an Arizona football fan.
But to know what I am referring to, what matters is what I am thinking when I say it, and the context in which I say it, not what others assume based only on what they personally think of when they hear the word "cardinals."
When I said "cardinals" I meant the baseball team. Baseball teams are not red birds, red birds aren't football teams, and football teams are not clergymen in red robes. Thus when I say cardinal in my context, and when the Pope says cardinal in his context, there is no reason to assume we mean the same thing. It doesn't matter that the baseball team was named after a bird whose color reminded someone of the robes of Catholic clergymen.
And it doesn't matter that Islam's Allah is an Arabic word derived from a Hebrew one for a Hebrew God, and that the Hebrew term El Shaddai is also one used in Christianity; the Islamic Allah is not the same as the Christian God, any more than my St. Louis baseball players are bright red birds. The Islamic god is a master of slaves; the Christian one and indeed the Jewish one has a relationship of Father to free people.
Neither does the Jewish. Would you have supported the walkout had this been a rabbi? Or are you ready to admit that this is a POLITICAL and not a religious gesture?