I also want to emphasize the fact that Hagia Sophia is no longer being used as a mosque. If it were then then the Muslims could claim that it would be unjust to deprive them of a place of worship. As it is, no harm would come to any Muslim worshipers.
The same places of worship continued in use and few sound structures were ever knocked down.
What I wonder is why, if their practice was to knock down Christian churches and put up mosques on the site, the Moslems left Hagia Sofia alone (for the most part), and even preserved the statuary?
Do you suspect that both the Moslems and the Christians in Spain were a better cut of human being than those in the East?
I was once touring Hagia Sophia in a group that included a couple from Saudi Arabia. The man wanted to pray, and the tour guide told him he couln't pray in the Hagia Sophia, but would have to wait until the group got to the Blue Mosque.
The Orthodox already have a huge church in Istanbul. I don't know whether they'd want to take on another one, since keeping it in shape would be extremely expensive.