I understand that not all the characters are religious. However, if a religion is mentioned in a character's bio, one should use it at least a little - even if it means to highlight that he has evolved and doesn't believe anymore, and that his current beliefs aren't the same with the ones he was taught in childhood. Not to have it written in the bio, then act as if it was never mentioned. Why bother then to mention it in the first place?

This is twice as valid when it is about somebody hiding his religion. There might be the desire to blend in, to seem unconspicuous and to deliberately not show any trace of the hidden religion. It makes perfect sense - but in the character's thoughts, there has to be this deliberate choice; an inner conflict, from time to time, between what he had been taught initially and what he has to do now. Or minor, delicate little things which still pertain to the hidden religion, even if they can't be directly traced to it.

For example, there are two NPCs, one muslim, one Jewish - in a time where Inquisition still existed and... burned.

The muslim one still believes in Allah as he had been taught, just that he can't say it in the open. He doesn't pray all 5 times a day, at least not visibly, but he surely says the  prayer in his mind when he can. He gets up earlier than the others he lives with, for the ritual ablutions. This means he is cleaner than others, and a little teased for it, but nobody makes the connection between a strange (for that time) desire for cleanliness and religion. He does abstain from eating pork as much as possible; but when he crossed the sea (and not as a passenger) to the colonies, he had to eat what the others did. Salt pork and hard tack was the general menu. As he is isolated from any other Muslims, he doesn't keep any holidays because nobody can tell him when they are (moon-based religious calendar).

The Jewish is a sailor; again, he does abstain from eating pork as much as possible; but when at sea, he can't. He eats with the others, so the notions of kashrut had to be forgotten. Even so, I think he'd never mix dairy and meat at the same meal, and he'd prefer drinking strong drinks or ale instead of wine (which, according to kashrut, is sacred and should have been only grown and harvested by Jews according to kashrut provisions). He also doesn't gamble, because he remembers from his bar mitzvah (the only torah studies he had ever done) that it is forbidden. He doesn't know much more than the basics about his own religion, so other precepts he might infringe in good conscience, without knowing. He also tried to avoid medical control aboard the ship whenever he could. At the transfer to a new ship he couldn't anymore, so he trembled what would happen when the doctor would discover the pledge of Abraham carved in his flesh. Fortunately for him, that particular doctor didn't care and didn't report.

These aren't much. Just little details to flesh up more a character over time - and taking into account that these are NPCs, even more than needed. But still something to make the characters more rounded and more believable. I wished others would do the same. The Jewish sailor's sister never had a moment of thinking about God, of conflicting thoughts or anything.

My Catholic characters, more or less believers, show their religious thoughts (or contempt towards them, for one who doesn't believe anymore). There is one who was once Catholic but turned Anglican because it was bad for business to be Catholic. He isn't much religious of any nature, still there are some inner conflicts within him between what he had learnt in his first school years with the monks and what he is doing now.

My point is that if you gave your character a religion, show it a little in his thoughts, deeds or habits.