I wonder if they would be willing to propose a resolution among their religious leaders recognizing the Christian celebration of Christmas. Their recognition and acknowledgment of the birth of Christ, the Son of God, would go a long way in patching the divide in the mutual understanding of the two religions.
I don't know a lot about Islam, but I highly doubt they dispute the fact that there was a guy walking around the desert named Jesus. But just as we don't expect the Jews to recognize Jesus as Christians do, I see no reason to expect Muslims to do that.
You know the answer to this. The Muslim religion was developed (reveiled) last to mankind. (This must really irk the Mormons.) Therefore, with regard to Judaism and Christianity, Islam is the religion to become, either by enlightenment or by the sword.
If Islam dropped this concept, and morphed into a religion that could live along with the other world's religions, AND IF THIS WAS STATED IN EVERY MOSQUE, then I could get behind a statement recognizing a High Holy period, and yes, I would expect the same for Rosh Hashanah and Yom Kipur.