I wasn't aware he was despised, films of him being introduced prior to his fights indicate he received a good hand from the crowd.
He was despised by people who knew him personally, or had to do business with him. He wasnt despised by the average fan. His popularity took a hit after the Fox debacle but at the time there was no proof so even then a lot of people just thought he was getting old and worn out. He was hugely popular in Detroit, Chicago, and to a degree in New York. Not a superstar but definately one of the leading lights.
I was at Madison Square Garden for the Quarry-Norton fight in 1975, and when LaMotta was introduced at ringside he received an ovation that was exceeded only by the one for Floyd Patterson.