Is Buddha nature active or passive?
Would anyone say that enlightenment means we can suffer (frustration) in an active way?
It depends on who perceives it, depends on what's being talked about, and it can be the both at the same time.
Eastern philosophy and spirituality is very different from our western logic. For us, it must be A or not A, for them it can be A and not A at the same time. In Shunryu Suzuki's "Zen Mind, Beginners Mind" there is a handful of paradoxes.
Coming back to the question, to the western mindset it seems that being active is good and being passive is bad. But it wouldn't be correct to assert that Buddhism is active just to say that it is good. So I prefer to say that enlightenment isn't one nor another. Or, in mystical terms, it is a balance between active and passive energies.
Meditation can look like a very passive practice, since you stay still, you stop moving, you stop talking, you calm down thinking and other mind processes. Then you stay there passive to noise, to itches, to mosquitoes, to pain, to chatter in the mind, to boredom, and so on.
Now, if you look from another perspective, meditation is very active. Nowadays people fill their days with activities, there is always something to do avoid tedium. Usually when someone starts meditating, it requires a great amount of effort to not move and to calm down the thoughts. People usually need to actively practice meditation to achieve subtler states of mind.
You will never listen someone saying something like "There was nothing to do and I was bored and then I suddenly realized that I was meditating."
Now, in enlightenment the underlying constant existential suffering isn't produced. It isn't fed, as if the ground of mind wasn't fertile for growing suffering. So if it doesn't exist, there can't be a relation of passivity or activity to it.
If you take mundane suffering such as physical pain or emotional pain, it keeps happening, but there won't be a "me" that feels pain. But there is just pain. You could say that enlightenment is passive because there is just a stream of phenomena that flows and between these phenomena there is pain. You could also say that enlightenment is active because there is complete presence and clear awareness of all phenomena that emerges, and nothing we judge as bad could produce the slightest suffering.
And finally, "active" and "passive" are just concepts. If you are taking the path to enlightenment, instead of trying to define it take the path to get there. And if you are just trying to define it, be warned that words and thoughts are too limited for this task.
Is the redness of an apple an active or passive principle? The true nature of the apple is that it has no absolute colour to be either active or passive, the perception of colour being born in interdependence, not of the apple itself, and as this is its true nature, is it an active or passive nature?
Some questions are slippery and invalid. Does a dog have Buddha nature?