Restore Mac from Time Machine while in Safe Mode. Password protected, not seen
Unlocking the WD My Passport External Drive probably neither works in Safe Mode nor in Recovery Mode because a custom 256-bit AES hardware encryption is used. The decryption/unlocking only works with WD Security for Mac or WD Drive Utilities for Mac installed.

You have to boot to Recovery Mode (hold cmdR while booting) erase your main OS X volume and reinstall OS X. 


Now you can either migrate the data with the Migration Asssistant:

Make a temporary admin user (different short user name than your backup) and then install the WD Security software. Then you can run Migration Assistant to read the files from the now-unlocked drive.

Once your migration is complete, you can leave things as they are or decrypt the WD drive and instead use Apple's encryption. That is supported at boot time so you don't have to do a dance when you erase and reinstall.

If you do that, the steps will be simply reboot to Recovery Mode and restore the Time Machine backup.
or use Time Machine to completely restore the Time Machine backup:

Install the WD Security software and completely remove encryption of the WD My Passport. Then reboot to Recovery Mode and use Time Machine to restore the backup.