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I have a feeling that perhaps in some sense politics is self-balancing. You attack things that are associated with your enemy, which means that your enemy will defend them. Assuming you are an entity that only cares about scoring political points, if your enemy uses rationality as an applause light, you will attack rationality, but if your enemy uses postmodernism as an applause light, you will attack postmodernism and perhaps defend (your interpretation of) rationality.
That means that the real risk for rationality is not that everyone will attack it. As soon as the main political players will all turn against rationality, fighting rationality will become less important for them, because attacking things the others consider sacred will be more effective. You will soon get rationality apologists saying "rationality per se is not bad, it's only rationality as practiced by our political opponents that leads to horrible things".
But if some group of idiots will choose "rationality" as their applause light and they will be doing it completely wrong, and everyone else will therefore turn against rationality, that would cause much more damage. (Similarly to how Stalin is often used as an example against "atheism". Now imagine a not-so-implausible parallel universe where Stalin used "rationality" -- interpreted as: 1984-style obedience of the Communist Party -- as the official applause light of his regime. In such world, non-communists hate the word "rationality" because it is associated with communism, and communists insist that the only true meaning of rationality is the blind obedience of the Party. Imagine trying to teach people x-rationality in that universe.)
I don't think it's necessary for 'rationality' to be used an applause light for this to happen. The only things needed, in my mind, are: