"cambiar de signo" is a mathematical metaphor based on the idea of a change of sign, whereby positive values become negative and vice versa (+1 becomes -1 and -1 becomes +1). It means that leftist positions "han sido cambiadas de signo", "have had their sign changed", that is, been changed from positive to negative or negative to positive; they've been inverted, rather like the idea of a mirror image. Actually, the idea that right and left and simply the inverse of each other is quite old.

I think "turned on their heads" or "stood on their heads" would fit quite well here:

"stand/turn something on its head
to make an idea or belief the opposite of what it was before
The first feminists simply took the accepted view that men were superior to women and turned it on its head."
http://idioms.thefreedictionary.com/stand on its head

The example in this definition is pretty close to what your author's talking about.

Of course you could also use "inverted", "turned back to front", or any other expression that implies reversal.

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Note added at 1 hr (2016-04-13 19:22:41 GMT)
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Actually "cambiar de signo" can be used more loosely than this, rather than its strict mathematical but it always implies radical transformation:

"el sentido y alcance del protagonismo estatal va a cambiar de signo, va a ser totalmente diferente"
https://www.google.es/search?num=100&q="cambiar de signo"&oq...

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Note added at 2 hrs (2016-04-13 19:36:59 GMT)
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An example or two from academic texts to illustrate this expression:

"Lately, all this has changed, and the politics of employing the term
culture have been stood on their head."
https://www.academia.edu/961669/An_Anthropology_Made_Safe_fo...

"In this reformed agenda, the so-called principles of constitutionalism must be stood on their head as they are applied to the governance institutions of the village."
https://books.google.es/books?id=8NGjyJ9HEoQC&pg=PA40&lpg=PA...