This is the shit the NSA should be worrying about. Securing the US IT infrastructure against nation-state intrusion. Not dragnets of everyone's naked selfies.
No, with a small caveat: If that civilian agency (say DHS) is connected to the GIG[1], then DISA has a say-so and can threaten to disconnect them for failing security audits.
Something to keep in mind is that the STIGs are merely implementation guides to secure a system. Therefore, different agencies have different interpretations. In some cases specific secure implementations break systems and applications (mostly legacy ones), so they avoid securing those particular settings all together.