The problem still exists as of 12.1.1:
➜ ~ wolfram
Mathematica 12.1.1 Kernel for Linux ARM (32-bit)
Copyright 1988-2020 Wolfram Research, Inc.
Mathematica 12.1.1 Kernel cannot find a valid password.
For automatic Web Activation enter your activation key
(enter return to skip Web Activation):
You will need to get a password from your
license certificate or from Wolfram Research
(http://register.wolfram.com).
Machine name: raspi2
MathID: 4703-79205-43531
You will need a valid activation key and password in order
to proceed. Go to http://user.wolfram.com to
register your activation key and obtain the password.
Enter your Activation key [format xxxx-xxxx-xxxxxx]:
Enter your password:
The password you entered is not valid.
Please press Enter to quit.
Adding the user to the video group fixed it for me. I figure adding full command output as above may help others (like a future me, once I've forgotten this) find this thread.
Edited to add: To fix the problem for the current user (regardless of that user's name), you can use:
sudo usermod -a -G video $(whoami)
