Problem is, the holy scriptures are from back then, and the fundamentalists of either religion who trouble the world and kill each other all feel called by those ancient scriptures like it were some timeless law cast in stone (which they actually claim to be). Judaism is founded on the Torah, Christianity on the NT on top of the Torah, and Islam on the Quran. Christian extremists like Evangelicals claim the bible's sole authority, Jewish extremists the Torah's, and Islamists the Quran's. If you're dogmatic about them, and reading them there's good reason to consider them dogmatic, there is little room for understanding and tolerance. Tolerance in the sense of accepting the other ones as equals, and not consider their belief idolatry and darkness of mind.
Why, when people talk about religion, does it always seem to go back to antiquity?
The present day should tell you what any religion is all about.
Jewish extremists who believe in God's ancient order to settle the lands of Canaan and slay the Canaanites may feel bound to settle in the West Bank and dislodge its inhabitants. Christian extremists may feel bound to spread the gospel to all the world, and not least to the Jews themselves (which they're not too fond of), and usually consider Islam some sort of devil worshipping. Christian extremists can be quite un-Christian about fighting other beliefs. I'm not sure what the particular Islamic "order" is, but it's probably also something that's likely to cause disagreement.
It'd be great if there were only moderate followers of each religion, who seem to get along very well in my experience, but the big trouble and instability is caused by extremists claiming the sole authority of their respective scriptures. I don't know if it's the same with Judaism and Islam, but Christian fundamentalism continues spreading, and with it, the belief in the bible's literal truth, which I'm very concerned about.
Point is, those ancient scriptures are so central and influential that imo you can't separate either religion from them.