NOTE: This question does not assume the existence or non-existence of free will.
Dan Dennett, Professor of Philosophy at Tufts University, states that when "...neuroscientists who've been going around saying that neuroscience shows we don't have free will...[are] doing some real harm". Dan Dennett: Big Think
He goes on to describe a (seriously flawed) thought experiment to support his claim, implying that those who learn there's no free will will be rendered "mentally incompetent", and that broadcasting such news would be "irresponsible".
Dennett references Vohs and Schooler, 2008 to support his views, but Miles, 2013, claims that Vohs and Schooler's studies, "...all appear to be linked by a fundamental methodological error that suggests that... their putative findings may be spurious". Miles also makes the vital point that, "And it has long been recognised by certain scientists, legal theorists, and philosophers that far from having prosocial benefits, belief in free will acts to discriminate against the poor and racial minorities, may make justice impossible and even encourages contempt for and violence towards the weak".
Dennett's generalisation - about our ability to healthily process the notion that free will is an illusion - is broad and condescending, but he may be right in that some, if not many people will be ill-equipped to cope with such information. It is easy to imagine some people becoming apathetic, criminal, nihilistic, depressed, negligent and/or reckless as a result of being told that they are cannot be held morally responsible for their actions.
Assuming it is possible to suppress a finding of such magnitude, would the dangers presented by such a discovery justify its suppression?
EDIT: In response to a comment request, I provide the following (admittedly imperfect) definition of free will:
"The ability to act and make decisions in a self-determined way, independently of causal or random physical processes; to be the originating source of one's own behaviour".
...and of the illusion of free will:
"To perceive that one holds free will when in fact one's actions and decisions are dictated by deterministic and/or random physical processes".
Any suggestions for improvement of these definitions will be considered.
I provide some other references useful to this consideration of this question. Whilst there is ample peer-reviewed material on this topic, I have emphasised generalist articles that are accessible without payment/subscription, in the hope these will provide further direction to the more academically-inclined.