You are right that pam shouldn't lead to gdm not working in any case. Knowing the context help to define the priority of the issue though.
The initial report/tools indicate that you are on 19.04, fingerprint authentification should work out of the box there (if you have a supported reader, which might be the issue, what device do you have?). That's probably worth another report (unless it's known/the device not being handled under linux)
You are right that pam shouldn't lead to gdm not working in any case. Knowing the context help to define the priority of the issue though.
The initial report/tools indicate that you are on 19.04, fingerprint authentification should work out of the box there (if you have a supported reader, which might be the issue, what device do you have?). That's probably worth another report (unless it's known/the device not being handled under linux)