We can reset the password while leaving security on.
The config.xml file in /var/lib/Jenkins/users/admin/ acts sort of like the /etc/shadow file Linux or UNIX-like systems or the SAM file in Windows, in the sense that it stores the hash of the account's password.
If you need to reset the password without logging in, you can edit this file and replace the old hash with a new one generated from bcrypt:
$ pip install bcrypt
$ python
>>> import bcrypt
>>> bcrypt.hashpw("yourpassword", bcrypt.gensalt(rounds=10, prefix=b"2a"))
'YOUR_HASH'
This will output your hash, with prefix 2a, the correct prefix for Jenkins hashes.
Now, edit the config.xml file:
...
<passwordHash>#jbcrypt:REPLACE_THIS</passwordHash>
...
Once you insert the new hash, reset Jenkins:
(if you are on a system with systemd):
sudo systemctl restart Jenkins
You can now log in, and you didn't leave your system open for a second.