Can children of the opposite sex share a bedroom?

You'll probably get this answer a lot. The rule I would go by is if it is necessary then I wouldn't let it go past elementary school. I would avoid past the age of 5 or 6 but if you HAVE to don't let it go on too long.

Are you asking from a legal or moral standpoint?

From a legal standpoint very few places have laws regulating this.

From a moral standpoint, it's a judgement call based on the sexes and ages of the children and their maturity level. It also depends on family finances.

Personally, I would put them in separate rooms before the oldest goes through puberty.