Does affecting an action card affect the Minion it has been played on?
Q: Does affecting an action card affect the Minion it has been played on?

A: No.

Q: Can an ongoing action card played on a minion be destroyed when an action played on a base is preventing minions from being affected?

A: Yes.

From the most recent rules (Pretty Pretty Smash Up), page 9:


  Affect: A card is affected if it is moved, returned, destroyed, placed, or is changed in power or controller, or has an action attached.


Removing an action is none of these. Even if you were removing an action that gave +2 power, the action doing the removal isn't changing the the minion's power.