Atheists are frequently challenged to explain why they are so critical of religious and theistic beliefs. Why do we care what others believe? Why don't we just leave people alone to believe what they want? Why do we try to "impose" our beliefs on theirs? Such questions frequently misunderstand the nature of beliefs or are even just disingenuous. If beliefs weren't important, believers wouldn't get so defensive when their beliefs are challenged. We need more challenges to beliefs, not less.
What is Belief?
A belief is the mental attitude that some proposition is true. For every given proposition, every person either has or lacks the mental attitude that it is true — there is no middle ground between the presence of absence of a belief. In the case of gods, everyone either has a belief that at least one god of some sort exists or they lack any such belief.
Belief is distinct from judgment, which is a conscious mental act that involves arriving at a conclusion about a proposition (and thus usually creating a belief). Whereas belief is the mental attitude that some proposition is true rather than false, judgement is the evaluation of a proposition as reasonable, fair, misleading, etc.
Because it is a type of disposition, it isn't necessary for a belief to be constantly and consciously manifested. We all have many beliefs which we are not consciously aware of. There may even be beliefs which some people never consciously some think about — but, to be a belief, there should at least be the possibility that it can manifest. A belief that a god exists often depends on numerous other beliefs which a person hasn't consciously considered.
Belief vs. Knowledge
Although some people treat them as almost synonymous, belief and knowledge are very distinct. The most widely accepted definition of knowledge is that something is "known" only when it is a "justified, true belief." This means that if Joe "knows" some proposition X, then all of the following must be the case:
- Joe believes X
- X is true
- Joe has good reasons to believe X
If the first is absent, then Joe should believe it because it is true and there are good reasons for believing it, but Joe has made a mistake for believing something else. If the second is absent, then Joe has an erroneous belief. If the third is absent, then Joe has made a lucky guess rather than knowing something. This distinction between belief and knowledge is why atheism and agnosticism are not mutually exclusive.
While atheists can't typically deny that a person believes in some god, they can deny that believers have sufficient justification for their belief. Atheists may go further and deny that it is true that any gods exist, but even if it is true that something warranting the label "god" is out there, none of the reasons offered by theists justifies accepting their claims as true.
Beliefs About the World
Brought together, beliefs and knowledge form a mental representation of the world around you — a belief about the world is the mental attitude that world is structured in some way rather than another. This means that beliefs are necessarily the foundation for action: whatever actions you take in the world around you, they are based on your mental representation of the world. In the case of theistic religions, this representation includes supernatural realms and entities.
As a consequence, if you believe something is true, you must be willing to act as if it were true. If you are unwilling to act as thought it were true, you can't really claim to believe it. This is why actions can matter much more than words. We can't know the contents of a person's mind, but we can know if their actions are consistent with what they say they believe. A religious believer might claim that they love neighbors and sinners, for example, but does their behavior actually reflect such love?
Why are Beliefs Important?
Beliefs are important because behavior is important and your behavior depends on your beliefs. Everything you do can be traced back to beliefs you hold about the world — everything from brushing your teeth to your career. Beliefs also help determine your reactions to others' behavior — for example their refusal to brush their teeth or their own career choices. All this means that beliefs are not an entirely private matter. Even beliefs you try to keep to yourself may influence your actions enough to become a matter of legitimate concern of others.
Believers certainly can't argue that their religions have no impact on their behavior; on the contrary, believers are frequently seen arguing that their religion is critical for the development of correct behavior. The more important the behavior in question is, the more important the underlying beliefs must be. The more important those beliefs are, the more important it is that they be open to examination, questioning, and challenges.
Tolerance & Intolerance of Beliefs
Given the link between belief and behavior, to what extent must beliefs be tolerated and to what extent is intolerance justified? It would be legally difficult (not to mention impossible on a practical level) to suppress beliefs, but we can be tolerant or intolerant of ideas in a wide variety of ways. Racism is not legally suppressed, but most moral, sensible adult refuse to tolerate racism in their presence. We are intolerant: we don't stay silent while racists talk about their ideology, we don't stay in their presence, and we don't vote for racist politicians. The reason is clear: racist beliefs form the foundation for racist behavior and this is harmful.
I don't think any one but a racist would object to such intolerance of racism, but if it's legitimate to be intolerant of racism then we should be willing to consider intolerance of other beliefs as well. The real question is how much harm the beliefs might ultimately cause, either directly or indirectly. Beliefs can cause harm directly by promoting or justifying harm towards others. Beliefs can cause harm indirectly by promoting false representations of the world as knowledge while preventing believers from subjecting those representations to critical, skeptical scrutiny.