"Home" translation in "hate has no home here"?
Try replacing '家' with the idiomatic '容身之所'

仇恨 (hate) 在这里 (in here) 没有 (has no) 容身之所 (place to stay)


仇恨在这里没有容身之所 (hate has no home here)

~
Or '立足之地'

仇恨 (hate) 在这里 (in here) 没有 (has no) 立足之地  (ground to stand on)


仇恨在这里没有立足之地  (hate has no place here)

Edit:
I believe an English slogan should still be a slogan after it was translated into Chinese.
I would translate the slogan “hate has no home here” to &quot;仇恨止步!&quot; (hate, stop!)  - It implies hate is not welcomed, therefore it has no place here.