It's not impossible, but given that a surprisingly large amount of conversational English expressions, particularly curse-words and the like, reference religion in some way or another, it is exceedingly difficult, to both remove them and have them flow in a believable manner. Another thing is why would the given culture(s) not have any religion/spirituality at all? I'm not entirely certain if it's all, but at least most human cultures throughout history have had their own religious/spiritual systems of beliefs/traditions/customs, so what makes those(ese) cultures(s) different? Do they put their belief in other things? If so, why, and why aren't those things regarded in the same sort of way religions tend to be? Is religion-as-such forbidden but a strong unshakable trust/belief in [the political system/science/work/natural processes/etc] okay? What caused religion-as-such to be taboo, or did it never become mainstream, and if not why not?

...tl;dr; as long as it makes sense within the confines of your world, and doesn't feel forced, go for it.