What does it mean to 'respect' someone's religion or religious beliefs? Many religious theists insist that their religion deserves to be respected, even by non-believers, but what exactly are they asking for? If they are simply asking to be let alone in their beliefs, that's not unreasonable. If they are asking that their right to believe be honored, then I agree. The problem is, these basic minimums are rarely, if ever, what people are asking for; instead, they are asking for much more.
The first clue that people are asking for more is demonstrated by the fact that no one who asks to be let alone is denied this and few Christians in the West have any trouble with their right to believe being infringed upon. The second clue that people are asking for more is how they accuse atheists of "intolerance" not because atheists are infringing on anyone's right to believe, or because they are going around badgering others, but rather because atheists are being very critical of the content of those beliefs. It can be argued, then, that what religious believers are really asking for is deference, reverence, high regard, admiration, esteem, and other things which their beliefs (or any beliefs, opinions, ideas, etc.) are not automatically entitled to.
Simon Blackburn describes this as "respect creep." Few if any irreligious atheists have a problem with "respecting" religion if we simply mean letting believers go about their rituals, worship, religious practices, etc., at least so long as those practices don't negatively impact others. At the same time, though, few irreligious atheists will agree to "respect" religion if we mean admiring it, having high regard for it as a superior way to live, or deferring to the demands believers make on behalf of their beliefs and practices.
According to Blackburn:
People may start out by insisting on respect in the minimal sense, and in a generally liberal world they may not find it too difficult to obtain it. But then what we might call respect creep sets in, where the request for minimal toleration turns into a demand for more substantial respect, such as fellow-feeling, or esteem, and finally deference and reverence. In the limit, unless you let me take over your mind and your life, you are not showing proper respect for my religious or ideological convictions.
Respect is thus a complex concept that involves a spectrum of possible attitudes rather than a simple yes or no. People can and do respect ideas, things, and other people in one or two ways but not in others. This is normal and expected. So what sort of "respect" is due to religions and religious beliefs, even from irreligious atheists? Simon Blackburn's answer to this is, I believe, the correct one:
We can respect, in the minimal sense of tolerating, those who hold false beliefs. We can pass by on the other side. We need not be concerned to change them, and in a liberal society we do not seek to suppress them or silence them. But once we are convinced that a belief is false, or even just that it is irrational, we cannot respect in any thicker sense those who hold it--not on account of their holding it.
We may respect them for all sorts of other qualities, but not that one. We would prefer them to change their minds. Or, if it is to our advantage that they have false beliefs, as in a game of poker, and we are poised to profit from them, we may be wickedly pleased that they are taken in. But that is not a symptom of special substantial respect, but quite the reverse. It is one up to us, and one down to them.
Respecting religion in the sense of tolerating it is usually a fair request; but such minimal respect isn't what religious believers usually want. After all, there is little danger in America of most religious beliefs not being tolerated on a basic level. Some religious minorities may have legitimate concerns in this regard, but they aren't the ones making the most noise about getting respect. Religious believers also don't appear to be interested in simply being "let alone" to go about their religious business.
Instead, they seem to want the rest of us to somehow admit or acknowledge just how important, serious, admirable, valuable, and wonderful their religion is. That's how they regard their religion, after all, and sometimes they seem unable to understand why others don't feel the same way. They are asking for and demanding much more than they are entitled to. No matter how important their religion is to them personally, they cannot expect others to treat it in the same way. Religious believers cannot demand that nonbelievers regard their religion with admiration or treat it as a superior way of living.
There's something about religion, religious beliefs, and theism in particular which seems to increase a person's sense of entitlement and the demands they make on behalf of it. People can act brutally in the pursuit of political causes, for example, but they seem to act even more brutally when they believe that they have religious or even divine sanction for that cause. God becomes an "amplifier" for whatever happens to be going on; in this context, even more respect, deference, and reverence is expected for religious beliefs and claims than other sorts of beliefs and claims which a person might have.
It's not enough that people in the religious community want something; God also wants it and wants it for them. If others don't "respect" this, then they are attacking not just the religious community, but also God the moral center of their universe. Here, "respect" can't possibly be thought of in the minimalist sense. It can't simply be "tolerance" and instead must be thought of as deference and reverence. Believers want to be treated as special, but irreligious atheists should treat like them like everyone else and, perhaps more importantly, treat their religious claims and opinions like any other claim or opinion.