Just as an FYI, I haven't seen this asked before, but I wasn't sure myself so I got a response through the FFG channel. The 'game state must change' rule applies to triggered abilities, and does not apply to attachments. For example, an attachment with +2 political can be played on a "-" dash political character.
Per Nate French:
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The “change in game state” rule applies to triggering abilities — this won’t prevent the playing of an attachment.
You can play the attachment on any legal card it can be attached to, even if it does not modify the character.