Number 3 is normal in all varieties of English, as far as I know.
Number 2 is grammatical, but has a different meaning: it implies that those people exist for the purpose of hating you, which sounds rather unlikely.
Number 4 is ungrammatical: 'who' refers to 'people', which is plural.
Number 1 is ungrammatical in my English, but is used in some dialects - typically some American ones, I think. In standard English, relative pronouns can be omitted if they are the object of the relative clause, but not if they are the subject.
Another possibility is
There will always be some people out there that hate you.
This is no different in meaning from number 3.