It is kind of a misused metaphor. For something to be happening at funeral speed means that it is happening slowly (funeral processions being very slow).
Someone can’t really hate you slowly so that is why it is misused.
Could it be that they mean they are hating you so fast that you’re having a funeral soon? In other words, they want to kill you or something like that?
I agree that it’s probably a misuse of an idiom meaning slowly, but perhaps what they meant was ‘hating’ in the sense of ‘slow burn’—evolving from mildly annoyed to moderately angry to extremely irate?
It relates to the speed of the cortege – which traditionally drives slowly from the deceased place of rest (e.g. home) to the place of burial/cremation. Passers-by should stop, doff their hats (if applicable) as a sign of respect and wait for the cortege to pass. It is also very bad form to overtake said procession.