1. I am a secular humanist. I have relatives who are religious. Some are nuns. Their faith is the right thing for them.
2a. Trying to speak outside myself; religion has been integral to human society for much of human history. You can kind of think of religious texts as being the very first law books. While science is useful to us, it does not provide definitive answers to the precise origin of life or the authority of one human over another. The humanist's society is seen as a cutthroat and uncaring place where authority is based on strength alone. The (mis)application of Darwinian theory to social philosophy is seen as one of the worst legacies of secularism and scientific thought. Because of this, secularism is seen as amoral at best.
When authority comes from a higher power, people are supposedly on an even plane. One contradiction in this is people who usurp God's authority as their own. How do humans apply the higher power's authority to shape their society without corrupting that authority? In addition, there are some disturbing (even terrifying) questions about <a href="http://www.tfproject.org/tfp/showthread.php?s=&threadid=26617">the continuity of consciousness</a> that can be addressed by appealing to the concept of the soul.
2b. The consent of the Government to allow en masse displays of religosity in facilities like public schools is seen as the threat the group poses to the individual. While religionists see the lack of prayer in schools as usurping their right to assemble, secularists see it as aggressive; the tyranny of the majority. If a class full of students are reciting the pledge and one student fails to say "under God"; that student may fear social retribution. Sometimes that fear is well founded.
Imagine yourself in the late 1950s as an Atheist or Buddhist in a school full of Christians. Do you refrain from "under God and risk a whole school thinking you a Communist spy? Do you speak against your beliefs out of fear of the people around you? Why did the Government create this social dilemma for you? If everyone like you spoke against their belief out of fear of the majority, the rights of the individual would be meaningless.
I think maybe this is a tension between the "democratic" and "republic" part of "democratic republic. The will or historical legacy of the majority is not the only thing there is.
Imagine if we could find scientific explanations for morality (compassion, altruism, empathy, etc), perhaps in Darwinism or some other theory. Would this understanding allow a rational society to be "more moral"?
Secular humanists learn sort of instinctive morality in childhood and then work to understand the scientific and philosophical basis of that morality. For us, morality is perhaps more a journey of scientific discovery rather than an set destination.
3. Recognising common aspirations and faults. Look at the previous paragraph. A secularist discovering the origin of their morality might fall into a crippling trap of total moral relativism.
Likewise a Christian might question their faith and why their Bible or Church leaders have made moral injuntions against certain things (ie, gay rights). If they're honest, religionists and secularists have the contradiction and ambiguity of their belief in common. Hey, it's not much; but it's a start. Let's find out whether maybe we have other stuff in common.