If you click the "Continue with Facebook" button on an Android device and get redirected to a screen that looks like this, then this article will help you fix it.
Steps to fix:
On your Android device, go to "Settings"
Then scroll down until you see "Apps" and then tap it
Then scroll down until you see "Facebook" and then tap it
Under "App Settings", you should see "Set as default". Tap it
At the bottom of the screen you should see "Go to supported URLs". Tap it.
Tap "Always Ask"
With that done, you just reset the default settings for clicking the "Continue with Facebook" link. Now when you go back to Chrome and click the button, it should prompt you to select which app to open it with. Choose Chrome. It should then redirect you to the login credential page for facebook.