Well look, if, by way of the scientific process, free will is shown to be an illusion, we not only would be better off believing in free will for the purposes of social order (in order to justify the justice system as it currently stands), we would also still
not be able not to believe in our own personal free will - there would be a fundamental disconnect between what we know to be the case and our own subjective experiences (as even current adherents of the no-free-will-theory still act as if they and everyone else has at least a modicum of free will). This is one way in which an unravelling of the mysterious might lead to alienation.
So, generally speaking, there are limits to the extent to which we can act on the conclusions of science and rational enquiry and argument. Another example: say that, by virtue of science establishing that the universe is infinite and through the process of logical argument, it was taken to be true that our personal actions cannot be said to be ethically good or bad
(infinitarian ethics), there is no doubt that we would decide to trump the scientific, rational process and ignore these conclusions (a kind of political correctness, if you will) as the behaviour then expected of us would go against the inherent grain of our nature - we would not be able to bring ourselves to act as if we actually believed it to be true (more alienation). This already happens: we attenuate or ignore the truth claims of science if we decide that they are generally unhelpful or if we cannot bring ourselves to act on them, and
this is not necessarily a bad thing to do!