Oh, yes!
But here is my feeling on this ...
... (and, please, Geerish, do Sit and Practice yourself and find for yourself "Buddha Nature". Do not be hamstrung or limited by my words if you disagree) ...
Buddha Nature reveals a truth about us and all things, always present, whereby there is no anger or killing or other violence possible (because no you and no me separate, so no doer and no done), nothing to steal or crave (for no separate things, thus no need or lack) . This is a Peaceful and Whole realm that, while right here, is often hidden by our divided thinking and the resulting selfishness, anger and frustration that we feel when our brains only see this samsaric world of separation.
In our Bodhisattva Vows, we "save the sentient beings" by letting the separate beings also experience such Fact. That is why it is sometimes said by Zen and other Mahayana Teachers that "we 'save the sentient beings' ultimately by showing them that, from the startless start, there were never truly any 'sentient beings' in need of saving, nor any lack to fill).
However, when you and I day to day must live in this samsaric world of "me and you", mine and yours, lack and need, win and lose etc. etc., things are a bit complicated. I do not feel that realizing the above Truth, even profoundly, means that we are necessarily going to live in this world free of the selfishness of our "little self." Until we are dead (and become what the Buddhists called "pari-nirvana' which is only the realm of "no me and you"), we are still people with human bodies, brains wired for selfish drives and instincts, fears, thoughts of past and future, judgments and divided ideas we need to survive, jealousies and all the rest of the human condition. Samsara.
Thus, Dogen (although most Zen teachers actually said about the same if you look carefully at their words and recommendations) spoke of "Practice-Enlightenment." The above realization of "no me-ness" helps avoid the selfishness and all the rest, but it is far from "automatic" by that alone in this world of "me-ness". (I bet a lot of the Rabbis and Christian mystics in the OP to this thread realized this too).
No, such realization frees the heart of much of the selfishness, and the excess desire, anger and frustration, fears and judgments, divided thinking ... but it is not automatic and, moreover, is not really helpful when we have to get up and live in this complicated world. (Small example: If your loved one dies or is injured in a terrible accident or crime ... realizing Buddha Nature may help one see beyond mere loss or death, it may help you forgive in one aspect, it may help free one of anger, it may allow one a sense Peace and no Loss ... but the human side may still cry in grief and ask why and feel some resentment and great loss. The two ways of seeing together produce great Wisdom and Compassion, but I would never want to give up either way of experiencing such an event. I want by Buddha Nature, but I also cherish my humanity. I want Peace, yet I want to cry ... I want to know Peace and yet cry with my broken heart at once.)
Realization will tend to make us more loving, more generous, more forgiving, more accepting, less fearful, less frustrated or angry and all the rest ... but, so long as we are in this world of Samsara, we are still humans who sometimes feel not like that.
So, Practice-Enlightenment is not an "automatic," but a realization (meaning, "to feel and understand in the bones") and a realization (meaning, "to make it real in each choice by our words, thoughts and acts") of Buddha Nature living in this complicated world. It does not make us saints or robots (perhaps somewhere down the road, 100000 lives from now when we are all perfect golden Buddhas, but not here in this life, in the muddy trenches of the front lines of this life for now). Now, we must simply realize Buddha Nature and do our best.
That is my view. Please find your own Buddha Nature.
Gassho, J
SatTodayLAH