Is there anything in the Quran or sunnah that either says believers should hate what Allah has prohibited or that good believers hate what Allah has prohibited? If so, please quote the relevant sahih hadith or Qur’an verse or excerpt of the sirah.
Yes. There are several such verses and ahadith which evidence that disliking sin is prescribed.
وكره إليكم الكفر والفسوق والعصيان
[Allah has] ... made hateful to you disbelief, defiance and disobedience
من رأى منكم منكرا فليغيره... فإن لم يستطع فبقلبه، وذلك أضعف الإيمان
Whoever among you sees an evil action, then let him change it ... if he cannot then [by hating it] with his heart – and that is the weakest of faith.
Haram “ not allowed” category has many things in it . Things you cannot consume , you cannot wear , you cannot do. Doesn’t mean you hate those things that are not allowed .
For example we are not allowed to consume pork . That doesn’t mean we hate the animal pig . We have to love all Allahs creations and purpose it serves . So there is many things are haram meaning not allowed but Allah doesn’t tell us to hate those things .