Those who do not accept atheism and naturalism fall into three categories.
There are those who don't believe any worldview is true, because they are agnostic about the big questions, and limit what they believe to what has been logically or empirically proved to a high degree of certainty. Such people refuse to speculate about where the universe came from, for instance, or whether there is a god or life after death. They simply stick to what they know for sure. But if they are inquisitive and reasonable, these people will end up believing all the same things naturalists do when it comes to how they should conduct their life, and so all they lose are the advantages of a worldview that answers the big questions and that provides a valuable platform for interpreting events and forming hypotheses.
Then there are those who believe there is something more to things than scientific naturalism allows, and hence believe in something supernatural, but who keep their supernatural beliefs so modest that these beliefs don't much affect their conclusions about how people should conduct their lives. They may have some false beliefs, but when it comes to making decisions, they either rely on the proven facts and don't let their supernatural beliefs interfere, or their supernatural beliefs just happen to entail exactly the same conclusions about how to act and live that naturalism does. Such people may be misled about some things, and we believe they'll miss out on many powerful revelations about how life and the world really work, but usually they will not produce any great difficulties for themselves or others.
But then there are those who have strong beliefs in the supernatural, and who are thus guided in making many decisions based on what we believe is not the truth. These people will be prone to accepting harmful beliefs that worsen the quality of their own lives, that prevent them from learning many great and valuable things, or that very often bring harm to others. For example, any religion that makes you feel bad about things that are not in fact bad is worsening the quality of your life. Likewise, any religion that discourages you from continuing to inquire and learn is stunting your mind and depriving you of the profound happiness of intellectual discovery. And any religion that encourages you to say or do things that hurt other people is a genuine public danger.
For instance, Orthodox Jews must follow such a detailed and strict code of conduct that their happiness is substantially impeded by their false belief that they have to endure those things to please a god who doesn't even exist. Likewise, Muslims can be misled into committing murder because of the false belief that a fictional god approves of it and will reward them for it. And many Christians cause real public harm by thinking homosexuals should be shunned or harassed or derided, because they wrongly believe an antiquated book, which tells them to do this, was inspired by a god.
We believe that any amount of supernaturalism in your beliefs is potentially harmful, because it means you are willing to believe things on insufficient evidence, and it means you are prone to misinterpret and thus misunderstand some events and phenomena. It also means you can be more easily manipulated or misled by religious leaders. And because of all those faults, you will eventually believe many false things (whether supernatural or not), and those who have false beliefs will make bad decisions affecting the happiness of others or themselves.
In fact, we believe the cultural trend toward exempting religious and supernatural beliefs from inquiry and criticism is a great public danger, for any belief that is exempted from inquiry and criticism can do real harm. If you are in any way prevented or discouraged from learning whether some claim or belief is false or misunderstood or misapplied, then you can easily be enslaved by false ideas. Naturalism gives no exemption to anything--no claim, belief, or authority is beyond examination, interrogation, or criticism, and therefore we find we stand a better chance of identifying false beliefs, errors, and misapplied wisdom.
Indeed, it is because we test all things that we have found all supernatural beliefs to be unwarranted. So the question being answered here may have it backwards. It's not just that denying atheism will have bad consequences (it certainly can--and has, as history shows in the divisiveness and often harmful consequences of religious belief). Rather, it is that, in our experience, if you adopt a fair and critical mind that seeks out and adopts the best methods of getting at the truth and rooting out error, you will invariably end up embracing naturalism and thus atheism--because that is where the evidence leads, once we subject it all to a proper and reliable test.
In contrast, we find that those who end up with beliefs in the supernatural do so only because they have not adopted or employed the fairest and most reliable means of finding the truth and avoiding error. And it is this very fact that produces the greatest danger, for people who use the wrong methods will make many mistakes about all manner of things, not just in matters of religion. And that is not good, for anyone. To learn more about the dangers of misplaced faith, see the Secular Web Library on: