Maybe it's "extraordinarity"? However, the word only has 5000 Google results.
Being a freak is not a good kind of __.
Noun The property or state of being extraordinary.
Also see this ELU question: What's a good word that means extraordinariness or exceptional-ness?
And just for the record the NGRAM shows extraordinarity virtually unused relative to extraordinariness :
I would say Deviation. Dictionary.com defines the word as "departure from a standard or norm." Since a deviation can be either positive or negative in nature, you're not being redundant when you call it "not a good kind of deviation." Deviation also carries a sociological connotation, which might be a point you're trying to make.
Extraordinaire can be drafted into service, but use with caution.
As a noun, it used to refer to a particular type of payment, and was also used as a shortened form of some job titles.
I have no problem with "a freak is not a good kind of extraordinaire."