MacBook Pro is constantly asking for an old Apple ID

See if you can recover the ID/password. Use every email address you can think of.

Apple ID - How to find your Apple  -  An iCloud e-mail address is an Apple ID.

Apple ID - Find  -       

If you forgot the Apple ID (iCloud) password, enter the Apple (iCloud) ID, and click Forgot Password. See if you can get a Rescue or Notification email option if necessary. Link to contact Apple Support at the end of the 2nd article.

Apple ID - Manage  -     

Apple ID – Forgot Password  *      

Or do a backup, preferable 2 separate ones on 2 drives. Boot to the Recovery Volume (command - R on a restart). Run Disk Utility/First Aid. Reformat the drive using Disk Utility/Erase. Use Mac OS Extended (Journaled), then click the Option button, and select GUID. Quit Disk Utility, then re-install the OS.

Reinstall from macOS Recovery

https://www.youtube.com/watch?v=HCrl_4k0aqo

OS X Recovery

When you reboot, use Setup Assistant to restore your data.

You are welcome. Merry Christmas to you.