I'm a lefty. I was most pleased to see that handedness is respected in this mod, for example, replacing my right arm with a cyber arm then installing a hand meant I couldn't use it. However, I then rectified this by placing a left cyberarm on me and removing my right cyberarm, which worked as expected. I then added a human right arm on and.... I can no longer select left handedness from the skin customization menu, it is forced back to right hand. Even though all the components are on my left arm, and it has enough power and production. Dying with keepCyberware off doesn't seem to fix it either. Restarting the instance in a single player world does.

I haven't tested this in a server environment.
Cyberware 0.2.11 and ReWIRED 1.0.9 are present.

Found this again in Robotic Parts v0.2.11.29. Left handedness in skin config as default. Added one cyberlimb then the other. Should've had right hand back, as I had charged afterwards. No idea why it didn't work.

This issue is closed. Open a new one with precise step on how to reproduce your issue.

Okay, turns out I just didn't have sufficient power.

Okay, time to write up a step by step on how to reproduce it. I had power, I was in a single player world, and I bet you I forgot a step in my report, because I did switch it from left to right at one point while my left arm was missing.
Step 1: Set handedness to left.
Step 2: install power, generation, right cyberarm, reinforced fist
Step 3: Left arm doesn't mine anything, as expected
Step 4: Attach left cyberarm, remove right cyberarm
Step 5: Left arm mines as expected, handedness cannot be chnaged to right hand because there is no right arm
Step 6: Reattach right arm
Step 7: Handedness is now forced to right arm and cannot be changed back to left, even though left arm is powered

The mod only read the handedness, it never sets it. It's more likely a bug in the base game, probably related to multiplayer as the setting is saved in your player data.
Also, remember that you'll switch to your other hand when you run out of power and only your main is augmented. The HUD will show a warning icon for your main arm when it happen.

Step 5: I can still change the handedness in the Skin customization menu. The active arm remains the left one because there's no right one. That works as intended.

Step 7: Right hand is now the active one. I can change the handedness in the configuration, but the render quickly switch back to the right hand. Options are forced back to right hand. That's a desynchronization bug.
Issue remains after creating a new world.
Issue isn't reproduced in the main menu.
Issue is reproduced by just removing the arm, no need to put a robotic arm or fist.
The mod changes the settings instead of the entity data, not sure if it's due to another issue.
As for this issue, it's not a network desync, it's a state leak in the mod when restoring your arm.
I've made a quick fix for now, but there's probably other bugs in the missing limbs handling.