The point is, those "very different ideas which contradict and compete with each other" don't compete at all. They co-exist as peacefully as the heels of professional wrestling do in their dressing room. Perfect peace, with nary a snarl to disrupt the absolute harmony!
Hey . . . that would make a great heel tag team--Charles Darwin and The Shaman!
Those Darwinians of today -- who Darwin may or may not have agreed with -- approach life from a materialistic point of view, and Buddhist approach it from a point of view that is anything but materialistic. What the two groups mean when they say that the self doesn't exist isn't the same thing.
Hegel, Marx, and Teilhard drew much more from the Judaeo-Christian tradition than from anything Hindu or Buddhist. If they argued that the self didn't in some way exist -- and I'm not sure they did -- it wasn't because Buddha corrupted them. There was plenty in their own tradition to work with.
And we could turn your argument around. A devout Jew or Christian may be a great believer in the self and soul. Ayn Rand, no believer in the soul, had as much belief in the self as Linda Kimball, the author of this article, has. Maybe somewhere in the world there is a Buddhist asserting that Ayn's and Linda's beliefs are all the same, all part of one great threat to Eastern civilization.
And check this out:
Cognitive scientist Daniel Dennett, one of the Four Horsemen of Atheism, claims there really is no you, that soul, spirit and will are illusions caused by chemical interactions in the brain while his partner in nihilism, naturalist Tom Wolfe proclaims, “Sorry, but your soul just died.” (The Spiritual Brain: A Neuroscientist’s Case for the Existence of the Soul, Beauregard and O’Leary, p. 4)
I'd have to read the whole article that Tom Wolfe, the journalist and novelist, wrote to be sure, but I don't think calling him Dennett's "partner in nihilism" really describes where he was coming from.