It's more of a cultural difference. Massacring Jews and Christians would've happened under an authoritarian regime anyway, unless that regime would be led by, say, a Christian, in which case there'd be a good chance of Muslims being threated like that (if government did have a say in this at all). Such things happen in places in the Middle East where the culture is at about the level it was 2000 years ago, and it's gonna take far more than government telling them "stop doing this" to really get rid of. If anything, a democracy would ensure that such a backwards idiot doesn't have all the power.
Is a democracy that abuses the rights of minorities truly better than an authoritarian regime that respects the rights of all groups?
Well, in that case, I'd actually be inclined to go with the latter. Democracy does have it's flaws, and an authoritarian regime that would respect the rights and demands of all groups (within reason, of course) would be a better solution. Now show me one such regime. Also, show me a somewhat benevolent authoritarian regime that stayed benevolent for more than a single ruler's lifetime. The major problem with monarchies and authoritarian regimes in general is that even if you do get a just, wise and overall good king/dictator/whatever, he/she'll die at some point, and there's no guarantee the successor won't turn out much worse.
A democracy gives you a stable, if medicore government, while an authoritarian regime gives you a roulette. You either get a good ruler or a bad one, and there's no way to change that. You could improve the odds somewhat (Rome did better under emperors than under senate), but that would require setting up a new system from ground up, which is impossible in the current world. Also, a democracy is somewhat more predictable on the international stage. Overall, it's the best option we have now, despite it's flaws.