Okay, so your character lives in a different timeline or on a different planet or something.
And every society has a culture. Every culture has at least one story about why things are the way they are.
These things are myths and religions in our world. And it’s probably unrealistic to have a society in a story where those things don’t exist (unless you are writing your story to make a point regarding myths and/or religions). Just because they haven’t heard of [insert any religious or mythological figure] doesn’t mean they don’t have their own version.
If you really want to flesh out your world, you gotta include a myth or religion. I don’t care if it’s how the flesh-eating pandas got their spots or how the world was created. You have to have something.
As long as your characters encounter at least one person with these beliefs, you’re pretty much set. You can have atheist main characters. But assuming they won’t run into someone who has different beliefs is ignorant. Unless they stay in one room the entire time, from birth to death, and never, ever encounter another being.
So how do you create a myth, legend, or religion?
A myth is generally something that explains how something happened.
If you have an unusual creature or race in your story, try to come up with a myth of how they became that way. It doesn’t have to be realistic. An example of this is an African story about how the leopard got its spots.
A legend is a story that’s about a particular individual who did extraordinary things.
Think about Hercules/Heracles. He’s a legendary figure. Or the story of Atlas and how he carries the world on his shoulders. Legends aren’t as necessary, but you can always have a character say something like, “Gee, he’s hunched over just like Atlas.” “Huh? Who’s that?” “Well, there’s this story from many years ago…” Many people compare others to legendary figures.
A religion is a set of beliefs and ideals. It may or may not have a large following. It may only be followed by one person, even. It may not be organized.
To create a religion, you need to come up with the foundation of why it was created. That means you need a religious icon that has done something amazing, and it’s been documented in some form or fashion. Your characters might believe that a woman with butterfly wings made the planet and imbued everything with her blessing, but she will curse you if you insult anything with wings like hers. These sorts of things have to be backed up with something. Maybe some guy insulted a butterfly for landing on his cake and ruining the icing. And then he died of a heart attack later that day. And then similar things happened to other people. So the people of that religion would be very careful not to say insulting things about butterflies and pixies and such.
These are character details. Religion affects how people live their lives. If a religion dictates that X will happen if you do Y, then the followers of it will not do Y if they can help it. If a religion says the followers must pray on the hour every hour (except for a few designated for sleep), then you can bet that the devout will do so.
If your religion is a big part of your life, then you can’t expect your characters not to have some kind of religion, too. If it’s not a part of your life, then you can’t expect everyone you create to be the same way. It’s fine if your character is or isn’t like you. Just be careful not to make everyone be your megaphone for your views.