In this chapter, Abraham returns to an old ruse, one he used disastrously back in chapter 12 of Genesis. Like then, Abraham's plan involves deception and causes harm to others.
So, what do we do when the people who hurt us claim to be God's people?
The first step is to determine if they really are God's people, sadly many charlatans abuse God's name for their own ends. Abraham was certainly God's guy, God even calls him a prophet in this text.
The second step is to remember that God's people are still flawed people. Redeemed they may be, but perfect they are not. They will fail, and those failures will at times harm others. This isn't God's fault, it is ours.
Lastly, what ought to come next is repentance and an attempt to repair the damage coming from God's people. In Genesis 20 Abraham does not repent, but God still requires that he be a part of the solution to fix what he has broken. If/when God's people fail, they ought to be the first ones trying to make it right.