I don't understand why people keep saying Ansible is idempotent. Ansible is not somehow magically idempotent, nor is Bash "always not idempotent". You can write bad, non-idempotent code in Ansible too and good, idempotent code in Bash too.

Sure, if you are using some of Ansible's modules that are developed specifically to be idempotent, then yes, but there are plenty of "shell" module examples out there that aren't remotely idempotent