Maybe those who *betrayed* what Sirius believes in (the cause of good, against Voldemort and his ilk) would not have gotten forgiveness from him - Peter and Regulus both. But Sirius not having a high opinion of Peter would be overridden by simple loyalty, if it were warranted. Betrayal is the ultimate sin in this series. Harry's unwillingness to forgive Ron in GoF is based in Harry feeling betrayed by Ron's disbelief. Snape is loyal to Dumbledore and the Order despite his personality conflicts with so many of the Order (especially Sirius). Godric Gryffindor's sword is delivered to Harry because of the loyalty he shows to Dumbledore in CoS. Barty Crouch, Jr. shows utter contempt for the Death Eaters who did not go to prison or die for Voldemort. Voldemort himself sees their lackadaisical approach to upholding the cause in his absence as betrayal. Etc.

Peter, being the Benedict Arnold in all of this, has sinned and won't be forgiven by either side. Voldemort may have awarded him for now, but Voldemort's memory is long and wicked.

I think Sirius *would* have died for Peter - while Peter was a friend, regardless of his personality or his quirks.