Didn't the Buddha preach "joyful participation in the suffering of the world"?
I don't know why some people can't understand how certain questions can cause one to embrace existentialism.
I think I can get my head around that notion, though I haven't seen it put that way. The basic story of Buddha's journey as I understand it was this: He was born into a rich family, but noticed that there were a lot of people who suffered. His family tried to prevent him from thinking about it by showering him with beautiful things and experiences, but he couldn't forget what he had seen. This is a sort of suffering, and no amount of wealth allowed him to forget it. He then left his family and undertook the opposite kind of life, living in a cave, starving himself, etc as was the way of the forest renunciants of the time. He came to understand that starving oneself lead to starvation, not salvation. So he undertook meditation and eventually discovered that suffering could be overcome, this was formulated in the four noble truths.
Fast forward some generations, there is a right hand path, where you attempt to deal with suffering by "getting above it" through withdrawal and meditation, the monastic tradition , like the Catholics. The book OPEN TO DESIRE points out that there is a "left hand path" which recognizes that suffering isn't really the problem, it is clinging to things that we like and running from things we don't that makes suffering persist.
So, it relates to existential approaches by taking WHAT EXISTS, and suggesting a way to deal with it. Suffering can be caused by the sublime. If you see a beautiful woman walking down the road, most of us here would like to get to the quick as quickly as possible, and we suffer if we cannot have access to the beauty immediately. That's how the whole escort business works, we get in the mood, we make a call, and we are serviced. But we might notice that even with the best sessions, they end and we eventually have to make another call. The Buddha was sexually serviced as an attempt to keep him in the palace, he noticed that no matter how often the concubines did their wonderful thing, it always ended and then there was suffering. So what would a more enlightened approach be?
There is a Zen story: two monks were walking through the forest and at a stream crossing they came upon a beautiful woman who was trying to cross the stream. The monk's rule was not to see/touch/think about women, lest they be tempted. Their practice was to avoid temptation in order to avoid suffering. But one of the monks picked the woman up and carried her across the stream, as that helped the woman with HER suffering. The two continued on for a while after leaving the woman. The monk who had followed his vow and not touched the woman had been thinking about the situation, and confronted the monk who had helped the woman, criticizing him for breaking his vow and touching her. He replied: "I put her down long ago, why are you still carrying her?"
The trick is to enjoy pleasure when you have it, let go when it is time to let go. Likewise, notice unpleasant things, and also notice that eventually they go away. That is very hard (or impossible), so what to do? You just practice noticing what is really happening in life. Pay careful attention to what exists in your life, notice how it makes you feel, notice how your thinking can make a feeling persist long after the situation that brought on the feeling on has ceased to exist. Meditation in the early stages is just practicing that.
So I get existentialism, and see Buddhism as compatible with it, as it is with science and psychology.
I tend not to read existential literature because it is great as far as it goes, but for me it doesn't really help make things better, it just makes you understand that you have to deal with what is actually happening without resorting to some belief system like Christianity or Capitalism to make sense of it. It can get caught up in making you look at suffering, and only suffering, and its teaching is learn to live with it because it isn't going away. What it often doesn't do is also point out that the beautiful thing at the heart of desire is still there, is still beautiful, and if we let go of it when it is time, it always comes back somewhere else. When my cat dies, I will miss him, but the goodness that I see in him will always exist. Every time a beautiful woman disappears from view, there is another along in a moment. I think in the end one finds that there IS meaning/purpose to life, and viewing it as clearly as possible makes it all worthwhile.
Sorry about the infodump, just got too much time on my hands at the moment.