I agree that radical Islamists are on the extreme right. I'm not sure I agree with your analysis of the left. You see protests against the Israeli government in Israel a lot more than you see them out of Israel. It's basically got a 20% approval rating in Israel at the moment. I have not seen those protests you're talking about where people aren't waving Palestinian flags, or chanting "free free Palestine", or "from the river to the sea". I don't consider that to be a left-wing peaceful protest against Israeli government and in support of freedom and human rights. You realize that "Free Palestine" is not going to be a safe place for gay people or anyone else. To me that's a front for militant nationalism. I think what we see on the (extreme?) left is some sort of neo-socialism that is anti-freedom or at least has a different priority order where freedom and human rights are below other items they consider more important. It's like left becomes right when you push hard enough which isn't a surprise. It's no longer liberal-democratic.

The speaker of the Knesset, from the ruling party, is openly gay ( https://en.wikipedia.org/wiki/Amir_Ohana ). And sure, Israel has its share of "backwards" people and we need to work on that.