Is everything you mentioned — that watching obscene cartoons is considered a sin requiring repentance, and that major sins require repentance — true?

You are right to condemn this person, for a true believer does not view sins from the perspective of their size, whether small or large, but rather from the perspective that they are disobedience to Allah the Almighty. Underestimating sins is a grave danger, for a person does not know when death will overtake them, nor whether their good deeds will be accepted and expiate their sins. Persistence in a minor sin turns it into a major one, requiring special repentance, and fasting alone will not expiate it.