Mum told Jude about his great-grandfather being a Cross to try to convince Jude that noughts and Crosses aren’t so different. They’re all human. But to Jude, that’s ridiculous. Crosses have never treated Jude well, and likely never will, even if they do know that he has Cross blood in his veins. Looks, Jude realizes, are all that matters, and this belief helps keep his society violent and segregated.