Learn English – I was once a fan of..? or I was a fan of…

Colloquially, you can be a fan (or not a fan) of anything, abstract or concrete, tangible or intangible.

When it's used colloquially, be a fan of implies "like".

I'm a fan of Tom Cruise. ~ The speaker is a fan of the actor. They surely like the actor.
I'm not a fan of spicy food. ~ The speaker doesn't like spicy food much.

Here is a good example showing that the expression "a fan of" can be used with virtually anything. It's from the movie Edge of Tomorrow (the quote is from www.moviequotesandmore.com):

[as they drive along the main road in France]
Cage: You don’t talk much.
Rita: Not a fan.
Cage: Of talking?
Rita: Not a fan of talking, no.

It just means that Rita doesn't want to talk (with Cage) in that scene.

So, your I am not a fan of negativity simply means: I don't like negativity.

It’s not necessary, but I’m not sure I’d label it as redundant.

I looked up redundant in a dictionary (NOAD), and found this definition:

redundant (adj.) (of words or data) able to be omitted without loss of meaning or function.

In English, many words can be omitted without a loss of meaning, but sometimes words are added for emphasis. Calling a word “redundant” makes it sound like it should be removed, and I’m not sure that applies to all superfluous words. (For example, if I say, “The room was very spacious,” is the word very redundant?)

Incidentally, the same dictionary defines the idiom once again as meaning “one more time,” so, in that regard, your sentence works fine grammatically. However, there’s an equivalent idiom that means the same thing – once more:

Personally, if it were me talking, I’d probably use one of these variants:

If you talk back to mother like that again...
If you talk back to mother like that once more...
If you talk back to mother like that one more time...

but I don’t find your original version with once again either particularly jarring or annoyingly redundant.