People will love you, people will hate you, and none of it will have anything to do with you. —Abraham Hicks
In this sentence what is the meaning of "will have anything to do"?
You need to understand the phrase:
to have something to do with (something/someone)
It means "to be related to something" or "to be the cause of something", or "being involved", but without mentioning in which way the two are related.
More information can be found here or here.
So, regarding your quote:
People will love you, people will hate you, and none of it will have anything to do with you. — Abraham Hicks
Meaning: The reaction of people (here: "love", "hate") will not be related to you (neither as a person nor regarding your actions).
(As far as grammar is concerned, please remember that "some" changes to "any" for negative phrases.)
None of it will have anything to do with you
It means that your decisions and actions won't change anything. It doesn't matter what you do, some people will hate you and some people will love you.
People will like you or people will hate you. You won't be responsible for the way people respond to you. We say "people take a liking to" someone, or they don't.