I'd assume that's a typo of "violence or hatred"

(Public INCITEMENTS to violence) of (HATRED against a group)

Capitalized the primary nouns in each phrase. Basically inciting people into hatred of a particular group, with violent connotations such as burning places of worship, etc.

Does that make sense in English grammar? In American English, "incitements of hatred" works, "incitements to violence" works, but they can't both apply to that noun and you're left with "violence of hatred".

It matters, too, because my suspicion is they want to punish hatred as though it were violence.

Well they might be, not sure. They're already punishing hatred in the mildest form with months of arrest across the UK.