Should they in an ideal world - no. In reality it saves a lot of bickering. If you mean having an affair - no way, that's a deal breaker.

Secrets are no good! Be with someone you don't have to keep any secrets from.

Everyone has secrets, and it's ok. Most people have done things in their past that they regret or would rather not share. Most of those things probably happened prior to marriage and prior to the relationship. Nothing good can come from divulging every detail about the past. Those are secrets, but the things the person is "guilty" of have nothing to do with the current situation. People learn and grow, so give the other person the benefit of the doubt. Ssecrets that have happened during the marriage is a different scenario though.