Do not wear shorts, or short sleeved shirts or blouses or tank tops, or skirts above the ankle, or pants or jeans.
Depending on the area you are in such as W. Jerusalem, you may be spat upon, assaulted or even stoned. While we would call that discrimination, there it is called roughly 'respecting the religious community'.
This applies to both the more religious Jewish and Muslim communities.
Don't necessarily be offended, think "when in Rome, do as the Romans": after all it is a sovereign country free to do as it pleases.
If you are using transit, you will be expected to ride at or near the back of the bus/shuttle.
Watch who you associate with, and definitely do not piss off anyone in a position of authority. The government of Israel is very paranoid, for obvious reasons.
Don't move there without visiting a few times first. Make sure you are comfortable there before doing so.
And for G_d's sake DO NOT talk Libertarianism or two-state solution politics when you are there. Great way to get blacklisted.