Hateful can mean "unpleasant; dislikable; distasteful:"[0] or "having or showing a desire to cause someone pain or suffering"[1]. For me its you that is intentionally loading the word.
One of the sources you provided has only one, clear, obvious definition: one that applies 99% of the time, and aligns with how they (and me, and I can assure you, every single reader of BBC.com) interprets the word.
The other source has practically the same definition listed as the top one, providing two alternatives, one of which is practically synonymous, and another showing an obscure alternative which is new to me and almost makes sense in the example sentence.
Yet they're loading the word.
Therefore sorry, but for me it's you who comes off as hateful. As in, unpleasant; dislikable [1]#2 :D
[0] https://www.dictionary.com/browse/hateful
[1] https://www.merriam-webster.com/thesaurus/hateful