One of the reasons I think Muslims make good stand-ins for Samaritans when Christians are reading themselves as stand-ins for Jews in Jesus' parables is that Muslims and Christians worship the same God to the same extent Samaritans and Jews worshiped the same God.
Muslims, according to both the Koran and the Bible, are descendants of Abraham through Ishmael. [See Gen. 25:12-18] Abraham and Ishmael shared some experiences together including sealing the first covenant. "On that very day Abraham took his son Ishmael and all those born in his household or bought with his money, every male in his household, and circumcised them, as God told him." [See Gen. 16-17] I wanted to provide citations to the Koran, but am not sufficiently familiar with the text and couldn't find a 'KoranGateway.com'
Of course, in Genisis it is Isaac who is offered as sacrifice, while the Koran reports it was Ishmael (Although, evidently not by name). You can read lots of mean stuff on the internet about which book is truly the inspired word of God. What I surveyed amounted to very rigorously identifying the twigs in the eyes of others. But, I don't think it is possible to deny that Muslims, Jews and Christians worship the same God.
We disagree about the nature of God; but frankly, I doubt the median Muslim view of God does not differ from the median Christian view of God any more than a Christian panentheist and a Christian supernatural theist. [See Marcus Borg's Outline for The God I Don't Believe In.] By the way, lots more hatred in the name of Jesus is available on the internet regarding Borg. Modern Pharisees are very opposed to those who see the world differently then they do.
In any case, I think the claim that Christians worship a different God from Jews or Muslims cannot be supported. I think it is just silly.