“Secular” people, by turning away from matters of faith and religion, are making a very specific philosophical choice that is equally considerate of society’s notions of the supernatural. I mean, it is their own reaction to religious ideas. If they are trying to “be a good person” by their own rules without caring whether or not a god exists, they are actually subscribing to a system of morals and beliefs. They don’t define themselves in relation to religious groups, even though they probably could.
I think it’s impossible to ignore the spiritual aspect of life for long. A crisis can push even the most ardent of believers to question their faith or non-faith in a god. A person who insists that they don’t want to relate their own personal beliefs to those of a group is being indifferent to the group, not to their internal moral and philosophical beliefs. Eventually, I think, most people strive to articulate their beliefs.
“Secular” is just another label that we can use to define our beliefs, but it doesn’t really relate to personal belief. A secularist is someone who believes that religion is not welcome in the public domain (politics, government, etc). A secular person or organization is one that practices this ethic by dissociating from religious organizations. Religion is different from faith. A secular person can be faithful to some higher being, but he or she will stay away from organized religion. But the faith (or non-faith) remains.
Forgive my ramblings. I’m not really an expert on this topic, so I expect to be burned at the stake for some of this.