Get any of the phones supported by LineageOS:
Good catch!
I believe they can, they claim is equivalent to getting your fingerprints or taking your picture.
So yeah, if enabling biometrics causes the phone to skip the PIN/password for convenience then better stick to just the PIN/password alone. You can always claim your right to be silent.
Possible loopholes:
Get a hold of a positive Covid test - if you already got the virus you don't need the vaccine.
Vaccine tourism - go on vacation to say Dominican Republic or Mexico, for some US $ you could get a 100% genuine certificate of vaccination without the vaccine.