Depends. Is there some sort of founding document that enshrines the right to vote and replace leaders with a regular cadence, regardless of the desires of that

Depends. Is there some sort of founding document that enshrines the right to vote and replace leaders with a regular cadence, regardless of the desires of that leader? If so, then regardless of who they vote for, it's a democracy. If instead a person is appointed to lead, who will use their religion to decide state matters, and there is no way to remove them except for them to choose to replace themselves, then it's a theocracy. "Theocratic democracies" are unstable and don't last. There is no way for them to last. Either it allows those who are not of the same faith as the leaders to influence policy and have their voices heard and becomes a democracy, or it doesn't, in which case it is a theocracy, and a form of autocracy or oligarchy (just, one that claims divine authority instead of purely material authority).