It was easy for literally everyone to believe Sirius was the rat because of what happened in fifth year (people who knew him from school used this as justification) and because Peter was just so timid and sweet and adored his friends.
This is actually canon but I needed you all to think about that.
Think long and hard about how deep Peter's betrayal goes.
Everyone believed a Black was capable, not a sweet boy. And James died thinking Peter was tortured for the information
Remus too. It really hits Remus hard because of how Sirius betrayed him in fifth year. Wasn't hard for him to think everything was a cover for Sirius being a death eater