how to use fingerprint id to sign in to apple ID
I would suggest you reset the Touch ID completely and add it back again. It can help you to fix the issue. 


Restart your Mac and hold down Command+R while it's rebooting to enter Recovery Mode
Launch Terminal.
Enter the following:

xartutil --erase-all

Press Return.
Type Yes when prompted to confirm.
Press Enter.
Quit Terminal.
Restart your Mac in normal mode.
Setup your Touch ID again and it should work.