Yes, it exists. And frankly 'minority privileged' exists in many ways too. Both have benefits and disadvantages. I would guess that being white probably has more societal advantages relative to minority privilege. But I certainly cannot be sure having only ever been white male and never a minority and therefore lack that ability to compare with full knowledge.
However, the 'fight' to fix this has been political for such a long time and I would think that initially, it did needed to be. Today, however, increasing 'minority privilege' is not going to decrease 'white privilege' at this point. We've reached a point of political diminishing returns, which needs to be recognized. Laws need to be in place to prevent any disadvantages, sure. But laws need to be removed that created advantages. The last 10% of society creating these privileges needs to be sorted out in society and punishing 100% for that 10% is only increasing that 10%.
On a side note, I'm not voting on your poll. My vote is 'yes', but we should not fix it with political means. The reason you have listed certainly doesn't describe me. Next time, stick to answers and leave the reasoning to us, if you want a true debate about the topics.