The Ottoman Empire ruled Palestine for a very long time - and Jews, Muslims, Kurds all co-existed in the Ottoman empire. (I'm also half Armenian, and we didn't fare quite so well, but that's another story, not necessarily connected with Islam). Of course, for political reasons Israel (like America) has never officially called it genocide. Turkey was too great a trading partner for Israel, and too important a strategic partner for the US. That may change, as the Knesset is reconsidering the question... particularly as they move closer to the Armenian Republic and further away from Turkey.
Political Zionism doesn't have much, other than preferential protection, for Judaism itself. Israeli courts aren't based on Halacha, but on civil law, law which draws more from British Common Law than anything else. It's more a Parliamentary Democracy than a Jewish state, per se. The key difference, of course, is that it offers preferential immigration rights to Jews or their recent descendants. The vast majority of Zionists believe that free exercise of ANY religion is important in the modern state of Israel.
As for not believing in God to be a Jew, technically that's true. It's more important to follow law in Judaism than pure belief. Also, as for "homos" - yes, Zionists also give freedom to other walks of life you might not find palatable. As do we here in NYC, but we also have many mosques, schools and believe America should be considered a safe place for Muslims.