The Relativity of "Normal"

I have found throughout my perusal of Katherine Dunn’s Geek Love and interesting binary within the text. This binary is the definition of normal. Not what is normal, but how is it defined in the context of the novel, how this definition applies to us as readers, and in a wider context as a society. It is a terrible faux pas to refer to a concept with anything so broad as the term ‘society’, but I think it is necessary to look at the giant amorphous mass that is our western civilisation and apply a GIL reading.
We have of course, Oly as one of our providers of definition, Arty as an extreme view, the Nuns which raised Miranda as well as Mary Lick as the other extremist, and Miranda.
These characters can be arrayed on a scale of definitions of normality, with Arty on the far left end, demanding that others must conform to his form or normality, Oly is to the left of the middle, Miranda to the right of the middle, the nuns to the right midway, and Mary Lick to the far right.

I-Arty-------------Oly----------I------------Miranda-----Nuns-----------Lick-I

So Arty, what do you think of them norms?
“Then there are those who feel their own strangeness and are terrified by it. They struggle toward normalcy. They suffer to exactly that degree that they are unable to appear normal to others, or to convince themselves that their aberration does not exist. These are true freaks, who appear, almost always, conventional and dull.”
And Oly?
They thought to use and shame me but I win out by nature, because a true freak cannot be made. A true freak must be born."

For the Nuns, we know that they try to persuade Oly to have Miranda’s tail removed, insist that she would be happier, and more normal. That she’ll be able to fit in.
Miranda, now she’s a harder nut to crack. As a child she prayed her tail would disappear, but as she grew older she came to enjoy it, and how it set her apart from others.
Mary Lick is quite a mirror image of Arty, although on the reverse side. While both she and Arty use their power, Arty his oratory skills and Lick her money, Lick urges the women to change what is natural about themselves to make them normal to a normie viewpoint – even to the degree of disfiguring them.

Now how does this reflect on us – and I say us as a western society comprised of normals -looking in on the freaks as we would a P.T. Barnum exhibit? Are we the true freaks, as Arty thinks, or should all freaks be made into Normals, as Lick would have us? Is there room for deviation, and is Oly in the right for denying Miranda a “normal” childhood?