I never really thought about it before but how do Sunni and Shia deal with Mecca? Do they go at different times or something?
The physical possession of Mecca by the Sunnis really chaps Shiite hides, but what can they do? Possession of Mecca is one of the great sources of power for the possessors. All muslims, of either main flavor, must follow the 2 pillars of Islam just the same. That is, the 5X daily prayer to the black moon rock, and the haj done around the black moon rock at least once in a life if a muslim is able.
About 30 years ago, a gang of shiite commandos/terrorists tried to take it over, after posing as pilgrims. (A common muslim trick, along with dressing as a covered woman, or using ambulances to transport bombs. IOW, they have no shame or honor, and consider them, in fact, to be decadent infidel traits proving weakness.)