This is important for a couple of reasons, and it's not really too hard to do. If however you are wondering how to complete this process this article should help walk you through the steps.
Notably, linking your Facebook account to the game is not in any way required. Not for finding and playing with friends, and not for saving data as long as you play on one device. There are benefits to it though. First, let's go through how to link the account.
You can link your Call of Duty Mobile account to Facebook two ways
There are a couple of ways to link the two accounts. Both are easy methods, but one is certainly more apparent than the other.
From the start screen
The first method for linking your Facebook account to the game can be done right from the start screen. As soon as you boot up the game, it should go through a series of progress bars and extra file downloads. Right after this, you get the start screen.
It's here that you'll have the option to link your Facebook account. The other option is to simply login to the game on a Guest account. Either option can be used to continue playing.
However, linking your Facebook account lets you carry your progress across devices. It also ensures your data won't be lost if there's an issue. If you've never played the game, such as in the beta, linking Facebook is the better option especially if you anticipate playing on more than one device.
In the settings menu
If for some reason you started playing with a guest account and then decided you wanted to link Facebook, you can still do so.
All you have to do is open up the game's settings menu and there will be an option there. This is a little more out of the way, so it's not as recommended as linking from the beginning, but it's there if players need it.
Furthermore, the end result is the same. From the game's main screen, tap on the settings menu button that looks like a little gear. It will be sitting in the top right corner.
Once inside the settings menu, look for the blue button in the top right corner marked "link." This will take you into the Facebook link screen. After you tap on the Facebook icon, it'll ask you if you want to link the selected account to confirm. And that's it.
Make sure to link the correct accounts
This might seem like a no-brainer, and it should be. However mistakes happen. While linking your Facebook account to Call of Duty Mobile is definitely recommended, make sure to link the right account.
As of now this will probably mostly apply to anyone that created a guest account during the beta, but is now trying to play the game on a different device. If you happened to do so, the only way to ensure you're linking the correct accounts together is to link your guest account to Facebook on the old device first.
After you've done this you should easily be able to login with Facebook on the new device from the start screen. This will make sure you continue on the new device with all your progress. Playing on multiple devices is also the best reason to link Facebook.
It doesn't appear you can transfer your guest account login from one device to another. So if you don't link your account to Facebook, you'll be starting from scratch. That's not the worst thing in the world, but if you have a ton of progress from the beta, it will be more than a minor annoyance to have to go back and complete it all over again.
There's seemingly no way to disconnect a Facebook account
The game doesn't seem to have an option to disconnect your Facebook account from your game account. Once an account is selected it appears to be permanent. At least until the option is added.
It's worth noting that disconnecting Facebook from Call of Duty Mobile on Facebook does not disconnect the game when inside the game. Even after doing so the game will still tell you that an account is already linked to that Facebook profile.
This leaves you with one potential course of action aside from starting anew. And that's contacting the support team from the in-game support menu. Even this might not result in a desired resolution, but if you happen to link the wrong account, or decide you want to link a different one, it's worth a shot.