It was nothing as widespread as 'public hate'. Do you realise how few people are interested in poetry? Think of the tiny percentage of the English speaking world who are interested in reading serious fiction, and divide that by a thousand.
TH got heckled at readings, Plath's grave was vandalised to remove 'Hughes' and he was criticised by academics interested in Plath's work for his heavy-handed, self-serving editing and destruction of her work, and, with his sister Olwyn, who took over the Plath estate, for the agenda-led way in which they tried to enforce their vision of Plath and the TH-SP marriage via de-authorising previously authorised biographies, browbeating biographers, refusing permission to quote SP or TH's work to those interpreting the marriage in ways they didn't like etc.
Janet Malcolm's brilliant The Silent Woman is wonderful on this, focusing on biographies and post-mortem mythologising of Plath, and specifically the virtual nervous breakdown experienced by Plath's authorised and best biographer Anne Stevenson, because of her treatment by Olwyn Hughes, who loathed Plath and felt she was protecting her brother and dictated the emphasis of much of the book to the point where AS put a note on the text describing it as a work of dual authoriship. (Neither JM nor AS were allowed to speak to TH, ever.)
TH behaved badly to SP, yes, that's beyond dispute. The awful thing that happened to him is to an extent what happens to all those on difficult terms with someone who dies by suicide -- he never got a change to redo, to make amends. Plath died young, hurt and furious at TH's infidelities, and it froze their relationship there. If she'd lived, they might have reconciled, or divorced, and she might have looked back on it as an unusually bad patch. Readers would view her life and work entirely differently. The difference between TH and other people adjacent to a suicide is that he had to continue to live with this publicly.
On the other hand, let's not get carried away. He did not avoid fame, he led an increasingly high-profile career as a public poet, ending up as Poet Laureate and best mate of Prince Charles.
And let's not forget either, that he benefited financially from the Plath estate. All the money earned by her writings came to him throughout his life. Plus Birthday Letters, his late collection about his marriage to SP was the fastest-selling poetry book in history. He became a rich man. For a poet, he became dazzlingly rich.
When he died, he left his substantial estate, £1.4 million, exclusively to his wife, Carol. Only in a letter, not the will, did he say he would leave the royalties from his own books to be divided between his children by Plath and his sister. Frieda Hughes took Carol to court for years after TH died, saying that the estate had stopped paying the royalties to her. The defence was that Carol had full control of the estate and the letter had no legal validity as it was not in the will.