Never go down from a ride in the middle of the road. The only possible option for you is to get down inside a settlement, after you've passed the security checkpoint. The only exception is Tzomet Gush Etzion, where it's easy to take a ride to Kfar Etzion, Efrat, Alon Shevut or the southern side of the area.
Don't enter a car while a person sits on the back seat, but you're being offered the front seat. Otherwise you may end up kidnapped by a militant group.
Get to know the locals. They will tell you about the safest places to go, and will sometimes even take you to the tourist spots by themselves. This will prevent you from strolling around and getting by mistake into a military camp.