Most secular parents I have encountered want to encourage their children to think critically. A likely result of critical thinking is that the children will not believe in God. Most secular parents do not want to engage in heavy-handed disparagement of religious belief similar to the heavy-handed disparagement of secular beliefs (or beliefs of other religions and denominations) exhibited by many religious parents.
One kind of critical thinking is to teach children about a variety of competing (and perhaps equally dubious) points of view. For example, many Christian children are told that the “Garden of Eden” story is literally true and explains how the universe, our planet, and our species arose. Children exposed to a variety of creation stories from a variety of cultures are much more likely to regard all such “tales” skeptically. Children like stories, and most children like to “act out” stories. (Acting also helps children gain confidence, especially very shy and introverted children.)
Below is a rough draft of a play-acting skit to help children learn about a variety of creation stories.
A play for children.
The Garden of Eden. Enter Adam, Eve, Serpent. God. [You know the story].
The Greek Creation Story. Enter Zeues, Hera, etc. [You know the story.]
The Norse Creation Story. Enter Odin, Thor, Freya, Heimdall, and the Loki. [You know the story.]
American Aborigine [Indian] Story. Enter Coyote, Raven, etc. [You know the story.]
Mesopotamian Story. The Babylonian Enuma Elish tells an ancient Mesopotamian story of creation. Apsu and Tiamat, fresh and salt water, mixed together, created the great and too noisy gods. Apsu wished to kill them, but Tiamat, who wished them no harm, prevailed. Apsu was killed, so Tiamat sought revenge. Marduk killed Tiamat and divided her, using part for earth and part for the heavens. Mankind was made out of Tiamat's second husband. [You may or may not know the story, so I stole a summary from the Internet.]
As you can see, we could go on forever, or at least as long as we have children who want to perform different parts.