Facetime and Messages also stopped working on my MacBook after I updated to Big Sur 11.1 on 12/22/2020. I tried this fix found online and it worked. Now my Facetime and Messages are working again on my MacBook. On your iphone: 1) Go to Settings - Messages app – Preferences – uncheck iMessage on icloud 2) Sign out of your Apple ID account 3) Sign back in with your Apple ID & password 4) Go back to Settings - Messages app - Preferences - enable iMessage on icloud again. Then try to open Facetime or Messages on your MacBook. They should work again. Mine did, not sure why or how but they did. Good luck!