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I think there are two kinds of mindfullness: observing while in meditation (and anything can be a meditation, like dishwashing, for ex. Focussing your awareness on what you're doing, whatever it is), vs. being mindful of one's motives for choices and action, and checking for egoic elements influencing us.
The first type one could call "passive" mindfulness--observing and accepting, but also bringing the awareness back to the object of focus when it wanders. The other, we might call "active" mindfulness, where the goal isn't acceptance of what is, it's the practice of non-attachment as a goal. It's about discerning whether our choices and actions are grounded in compassion and "virtue" as the Buddha defined it, or whether ego-clinging is creeping into our motives.
Mindfulness isn't always about acceptance; mindfulness has a corrective function as well.