Mussolini made the trains run on time
He was the leader of a fascistic party, which merged with the New Britain Party. So yes, given some of the things he said over the years, it is pretty certain that he did hate those people.
You'll probably tell me that my grandfather hated anyone who wasn't white, or English. After all, he thought Enoch Powell was a great bloke because of his (later) immigration policies, could rant about Germans till the cows came home, looked down on the French, etc.
But he married a half-Danish woman, got on tremendously well with her Danish family, & when his youngest daughter was seeing a bloke from Wiltshire he disapproved of, started bringing home a younger colleague he particularly liked, & trying to engineer occasions for the straying daughter to to be alone with said colleague. The colleague was Pakistani.
You're assuming that particular opinions belong to a set of linked attitudes common to people you loathe. In reality, those attitudes are often not linked. Someone can be an extreme right winger in many respects, as my grandfather was, but also have some very left wing opinions; a dislike of immigration, particularly non-white immigration, can go along with warm personal relationships with members of the disliked groups, even to passing the "Would you let your daughter marry one?" test.
The crude assumption that Moore hated women, etc. is based on this false grouping of attitudes into sets. In reality, people are much more complicated than that. There are sets of apparently contradictory attitudes which are common. Some people fear the other, & translate that into a dislike of black/Muslim/whoever people, but are perfectly nice to individuals. They don't really hate the group, they're just frightened by strangeness, & people they've met are no longer strange. This is just one of many ways in which the "If you're a woman he hated you" trope can be (& in Moore's case undoubtedly was) wrong.
PS. Don't assume that I approve of my grandfather. He really was a bastard. But like most bastards, not 100%.