This isn’t a news story, its just some blogger trying to start an online petition.
Online petitions are, as a rule, worthless. They provide individuals with the illusion that they are doing something productive, but such petitions are routinely ignored by government officials because there is no way of verifying that the “signatures” are from real people.
And in this particular case, the cause is already lost. As others have noted, Hagia Sophia is currently a museum. It has that designation because the nation of Turkey is officially secular and it strives to avoid endorsing religions. Many other formerly religious sites in the country have been turned into museums or similar secular function.
If Hagia Sophia were to revert to religious use, it most likely would be to that of a mosque since that is what it was before the collapse of the Ottoman Empire. And also because Turkey is predominantly a Muslim country.
Any de-secularization effort, if is to have any chance, will need to involve high level government and religious officials. Such an effort is currently underway to re-open the Theological School of Halki. Online petitions, however, will just go into the wastebasket.