The term secular society is often used to describe a society in which religion is a private affair and does not have an impact on politics or public life outside of the religious sphere. I've often heard humanists advocating secularism and saying that they have no problem with private religion.
Although this sounds ideal, I struggle to understand how private religion is possible. It seems to misunderstand the meaning of religion. I can't understand how anyone could be serious about their religion and yet not have it strongly inform their opinions. When someone holds a viewpoint because they believe it is based on a revealed truth, there doesn't seem to be any way to explain their opinion in a secular manner. I really can't imagine a society in which religious leaders voluntarily stay out of political and ethical debates or restrict themselves to secular viewpoints. I know there are religious secularists, but I don't understand how this can work in general.
There was an interesting BBC radio programme on this topic as part of the Beyond Belief series. Julian Baggini argues for secularism and doesn't address this issue to my satisfaction. Baggini does seem to acknowledge that you can't keep religion out of the picture completely.
I find myself conflicted in that I completely respect the right of others to be religious unless it has an impact on public life. This seems to be a contradiction. I want a society in which religion has no place in public life, but from what I understand of religion, this means a society in which their is no religion (or in which religion is unwillingly repressed, which is definitely not a good idea).
If I'm honest I have to say that I would like to see humanity achieve a non-religious society. I do respect people's right to have religious beliefs, but I also wish they'd hurry up and work out that their beliefs are daft so we can get on with developing a grown-up society.