I'm not sure he ever 'hated' HalfBloods- only those who sympathised with Muggles. Even PureBloods like the Weasleys were labelled Blood Traitors for their sympathy for the Muggle community.

Good question

@The Dark Marc OK, hated might not be the right word but he said a wizard/witch with one magical and one non magical parent was an abomination

I can't recall the exact speech he gave- but I think you're refering the 'dinner' speech at Malfoy Manor, where Voldemort voices his disgust that a wizard might actually want to breed with a Muggle- and that idea was repulsive to him.

My understanding is that those who had been born Half Blood but hated Muggles were just as welcome to follow Voldemort as any other.

I suppose that his father was a muggle, and once he figured out that he left them (Voldemort and his mom) he gained hate for them thinking that every non magic folk is horrible.

Voldemort (mistakenly) believed that the only reason Tom Riddle Senior left Merope Gaunt was because she was a witch and that possibly she died of a broken heart, leading him to be raised in a Muggle orphanage where he had a (let's say) troubled relationship with the other children.

All of this seems like a perfect recipe for someone to despise muggles and those who sympathise with them. Let's not also forget that the Gaunts, his mother's side of the family, were also big supporters of blood purity, a sentiment that had long existed since the International Statute of Secrecy was enacted.

Imagine how it would feel to learn your father left you and your mother because of your heritage, that she died soon after, and to spend so long feeling like you don't belong...

Even worse, imagine you then discover the history of a certain person who also harboured resentment towards people like that father and like those people who made you feel different. Imagine that person was powerful, and sought to overcome the struggles you faced, and almost succeeded. Imagine you discovered... Gellert Grindlewald.

Gellert Grindlewald who was concerned with blood purity, Gellert Grindlewald who believed wizards superior to muggles, Gellert Grindlewald who attempted to lead wizardkind into war with muggles.