There is a major "dangerous" scientific idea in contemporary physics, with a potential impact comparable to Copernicus or Darwin. It is the idea that what the physics of the 20th century says about the world might in fact be true.
Let me explain. Take quantum mechanics. If taken seriously, it changes our understanding of reality truly dramatically. For instance, if we take quantum mechanics seriously, we cannot think that objects have ever a definite position. They have a positions only when they interact with something else. And even in this case, they are in that position only with respect to that "something else": they are still without position with respect to the rest of the world. This is a change of image of the world far more dramatic that Copernicus. And also a change about our possibility of thinking about ourselves far more far-reaching than Darwin. Still, few people take the quantum revolution really seriously. The danger is exorcized by saying "well, quantum mechanics is only relevant for atoms and very small objects...", or similar other strategies, aimed at not taking the theory seriously. We still haven't digested that the world is quantum mechanical, and the immense conceptual revolution needed to make sense of this basic factual discovery about nature.
Another example: take Einstein's relativity theory. Relativity makes completely clear that asking "what happens right now on Andromeda?" is a complete non-sense. There is no right now elsewhere in the universe. Nevertheless, we keep thinking at the universe as if there was an immense external clock that ticked away the instants, and we have a lot of difficulty in adapting to the idea that "the present state of the universe right now", is a physical non-sense.
In these cases, what we do is to use concepts that we have developed in our very special environment (characterized by low velocities, low energy...) and we think the world as if it was all like that. We are like ants that have grown in a little garden with green grass and small stones, and cannot think reality differently than made of green grass and small stones.
I think that seen from 200 years in the future, the dangerous scientific idea that was around at the beginning of the 20th century, and that everybody was afraid to accept, will simply be that the world is completely different from our simple minded picture of it. As the physics of the 20th century had already shown.
What makes me smile is that even many of todays "audacious scientific speculations" about things like extra-dimensions, multi-universes, and the likely, are not only completely unsupported experimentally, but are even always formulated within world view that, at a close look, has not yet digested quantum mechanics and relativity!