I've been working on improving backstabbing penalties, because the way they currently are (mostly by Firaxis choice) is...lacking in terms of nuance. 
Examples of silly situations that can currently happen:
- Poland backstabs France by declaring war on them. You decide to join Casimir in backstabbing France, but take a large diplo hit with Poland for doing so.
- Rome is backstabbed by the Shoshone, your friend. You decide to backstab the Shoshone in retaliation. Rome gets mad at you and you take a large diplo hit.
- Montezuma declares war on several of his friends and razes their cities to the ground; but gets mad at you for denouncing, or being denounced by, one of your friends.
- Egypt gets mad at you for backstabbing Ethiopia, even though Ethiopia is Unforgivable to them and captured their capital, Thebes.
- You ended your Declaration of Friendship with Carthage via the Discuss menu. Every civ in the game considers you an untrustworthy friend, even Carthage's enemies. You then destroy all of Carthage's cities and eliminate them. Everyone considers you trustworthy again.
- You break promises not to attack Babylon and their protected City-State. This doesn't affect their willingness to be friends at all.
- In multiplayer, where a Declaration of Friendship is required to trade Gold with other humans and cannot be revoked except through war, you take major diplo hits with every AI for breaking it.
To avoid these kinds of situations, I'm reworking the backstabbing penalties. I will post my new idea for a rework shortly.
Also, I'm working on a system of putting penalties on a timer rather than having them be permanent, although the worst penalties (especially declaring war on friends) would last much longer.
If you have any feedback on your current issues with backstabbing penalties and how they could be improved, please post them here.

Examples of silly situations that can currently happen:
- Poland backstabs France by declaring war on them. You decide to join Casimir in backstabbing France, but take a large diplo hit with Poland for doing so.
- Rome is backstabbed by the Shoshone, your friend. You decide to backstab the Shoshone in retaliation. Rome gets mad at you and you take a large diplo hit.
- Montezuma declares war on several of his friends and razes their cities to the ground; but gets mad at you for denouncing, or being denounced by, one of your friends.
- Egypt gets mad at you for backstabbing Ethiopia, even though Ethiopia is Unforgivable to them and captured their capital, Thebes.
- You ended your Declaration of Friendship with Carthage via the Discuss menu. Every civ in the game considers you an untrustworthy friend, even Carthage's enemies. You then destroy all of Carthage's cities and eliminate them. Everyone considers you trustworthy again.
- You break promises not to attack Babylon and their protected City-State. This doesn't affect their willingness to be friends at all.
- In multiplayer, where a Declaration of Friendship is required to trade Gold with other humans and cannot be revoked except through war, you take major diplo hits with every AI for breaking it.
To avoid these kinds of situations, I'm reworking the backstabbing penalties. I will post my new idea for a rework shortly.
Also, I'm working on a system of putting penalties on a timer rather than having them be permanent, although the worst penalties (especially declaring war on friends) would last much longer.
If you have any feedback on your current issues with backstabbing penalties and how they could be improved, please post them here.