From a practical standpoint, this is a bad idea.
The secular world has chosen a calendar set by the Roman Catholic Church for its standard. Why? Because it was the Catholic calendar that made the necessary calculations to keep the seasons and astronomical events consistent from year to year-- the key advantage of a solar calendar. When the calendar they originally used (based on the secular Roman republic calendar) went out of phase, Pope Gregory fixed it.
The Jewish calendar also strives for it, but it's based on a lunar calendar. So, instead of a leap day every few years, they have a whole leap month every few years to keep in phase with the earth's orbit. (The scheduling of Easter is the last remaining relic from the Jewish calendar on the Christian liturgical calendar.) Obviously, having some years a whole month longer than others could be a big problem. Still, the difference in days is small enough that it makes acknowledging Jewish holidays within the Christian calendar at least feasible.
Now, compare that with the Muslim calendar. Just to give you an idea of the complete scientific ignorance of Islam, the Quran explicitly forbids leap-years, saying that those that follow it are being "led into error." Their calendar is based loosely on the lunar calendar, which is a full eleven days short of a full solar year. That means every 16 years or so, the Muslim holidays happen in a totally different season than at the start. If Ramadan occurs in the summer, 16 years from that point it will be in the winter. In the areas of the world where the seasons aren't significant, that's not a big deal. In temperate climates-- it's a pretty big deal.
Naturally, for those following a solar calendar, the two are completely incompatible.